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What integration technique?

Total questions: 84

Worksheet time: 7hrs 0mins

Name
Class
Date
1.

ln x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
2.

What method? csc⁡2 x\csc^2\ x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
3.

sin⁡ x cos⁡ x\sin\ x\ \cos\ x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
4.

(4x−16)12\left(4x-16\right)^{12}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
5.

x2 cos⁡ 5xx^2\ \cos\ 5x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
6.

1sec⁡ 4x\frac{1}{\sec\ 4x}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
7.

2xx2+1\frac{2x}{x^2+1}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
8.

1x2−25\frac{1}{x^2-25}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
9.

e−4xe^{-4x}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
10.

e−9x−3e^{-9x-3}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
11.

tan⁡ x\tan\ x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
12.

cos⁡(−x)\cos\left(-x\right)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
13.

cot⁡2(x+1)\cot^2\left(x+1\right)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
14.

sin⁡2x\sin^2x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
15.

x5 ln⁡ 2xx^5\ \ln\ 2x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
16.

e(7x−1)e^{\left(7x-1\right)}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
17.

(4x−1)4\left(4x-1\right)^4

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
18.

(11x+π )3\left(11x+\pi\ \right)^3

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
19.

sec⁡2x  tan⁡2x ,    u=tan⁡x\sec^2x\ \ \tan^2x\ ,\ \ \ \ u=\tan x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
20.

5xx2+10\frac{5x}{x^2+10}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
21.

2x2^x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
22.

1sin⁡2 7x\frac{1}{\sin^2\ 7x}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
23.

csc⁡2 (5x+π )\csc^2\ \left(5x+\pi\ \right)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
24.

1(x+3)2\frac{1}{\left(x+3\right)^2}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
25.

(x2)4\left(x^2\right)^4

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
26.

−sec⁡2 πx-\sec^2\ \pi x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
27.

ex−4e^{x-4}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
28.

ln⁡(2x+1)\ln\left(2x+1\right)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
29.

x ln⁡xx\ \ln x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
30.

1cos⁡25x\frac{1}{\cos^25x}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
31.

1(x+2)(2x−1)\frac{1}{\left(x+2\right)\left(2x-1\right)}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
32.

ecos⁡x sin⁡xe^{\cos x}\ \sin x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
33.

csc⁡2( 3x)\csc^2\left(\sqrt{\ 3}x\right)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
34.

( 2+4x)5\left(\sqrt{\ 2}+4x\right)^5

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
35.

tan(3x+2)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
36.

cot x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
37.

x3\sqrt[3]{x}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
38.

x exx\ e^x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
39.

tan⁡2(2x)\tan^2\left(2x\right)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
40.

7e(4−2x)7e^{\left(4-2x\right)}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
41.

sin⁡xcos⁡(x)+4\frac{\sin x}{\cos\left(x\right)+4}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
42.

525x2−4\frac{5}{25x^2-4}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
43.

cos⁡x sin⁡7x\cos x\ \sin^7x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
44.

sin⁡2(x4)\sin^2\left(\frac{x}{4}\right)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
45.

12x−1\frac{1}{2x-1}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
46.

2x−7\frac{2}{x-7}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
47.

sec⁡23xtan⁡3x\frac{\sec^23x}{\tan3x}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
48.

54x2−1\frac{5}{4x^2-1}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
49.

sec⁡2x\sec^2x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
50.

5x5^x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
51.

cot⁡7x\cot7x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
52.

cos⁡2x\cos^2x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
53.

e3xe^{3x}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
54.

csc⁡2x\csc^2x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
55.

cot⁡2x\cot^2x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
56.

sin⁡(15x)\sin\left(\frac{1}{5}x\right)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
57.

x csc⁡2xx\ \csc^2x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
58.

x e−xx\ e^{-x}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
59.

x5 ln⁡xx^5\ \ln x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
60.

csc⁡2(−5x)\csc^2\left(-5x\right)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
61.

102x−1\frac{10}{2x-1}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
62.

5x2x3−9\frac{5x^2}{x^3-9}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
63.

cos(2x-1)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
64.

1x+5\frac{1}{x+5}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
65.

10x+3(x+7)(2x−1)\frac{10x+3}{\left(x+7\right)\left(2x-1\right)}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
66.

x(x+3)2\frac{x}{\left(x+3\right)^2}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
67.

e2xe2x−1\frac{e^{2x}}{e^{2x}-1}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
68.

etan⁡x sec⁡2x,     u=tan⁡xe^{\tan x}\ \sec^2x,\ \ \ \ \ u=\tan x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
69.

1csc⁡6x\frac{1}{\csc6x}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
70.

x4+1x5+5x\frac{x^4+1}{x^5+5x}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
71.

52x+3\frac{5}{2x+3}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
72.

x2cos⁡2xx^2\cos2x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
73.

x sec⁡2xx\ \sec^2x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
74.

4e10x4e^{10x}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
75.

sin⁡x cos⁡3x\sin x\ \cos^3x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
76.

e−2x sin⁡xe^{-2x}\ \sin x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
77.

sin (3x)

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
78.

tan⁡2x\tan^2x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
79.

1x(5x−4)\frac{1}{x\left(5x-4\right)}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
80.

x cos x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
81.

32+x2\frac{3}{2+x^2}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
82.

5 4−x2 \frac{5}{\sqrt{\ 4-x^{2\ }}}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
83.

5x 4−x2\frac{5x}{\sqrt{\ 4-x^2}}

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts
84.

5arcsin⁡x5\arcsin x

a)
Standard integrals & reverse chain rule
b)
Partial Fractions
c)
Trigonometric identities
d)
u' f(u) substitution
e)
Integration by parts

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