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Integration by Substitution Practice

Authored by Cory Barnes

Mathematics

11th Grade

CCSS covered

Used 16+ times

Integration by Substitution Practice
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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the antiderivative:

∫(3x4+2)4(12x3)dx\int(3x⁴+2)⁴(12x^3)dx

12(3x4+2)4+C\frac{1}{2}(3x⁴+2)⁴+C

(3x4+2)4+C(3x⁴+2)⁴+C

15(3x4+2)5+C\frac{1}{5}(3x⁴+2)⁵+C

13(3x4+2)6+C\frac{1}{3}(3x⁴+2)⁶+C

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the antiderivative:

∫ x3(x4+3)2 dx\int_{ }^{ }\ x^3\left(x^4+3\right)^2\ dx

13(x4+3)3+C\frac{1}{3}(x^4+3)^3+C

112(x4+3)3+C\frac{1}{12}(x^4+3)^3+C

34(x4+3)3+C\frac{3}{4}(x^4+3)^3+C

14(x4+3)3+C\frac{1}{4}(x^4+3)^3+C

3.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the antiderivative:

∫6x(x+2)dx\int6x\left(x+2\right)dx  

6x2+12x+C6x^2+12x+C  

x2 −2x+Cx^{2\ }-2x+C  

3x2+6x+C3x^2+6x+C  

2x3+6x2+C2x^3+6x^2+C

4.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the antiderivative.

∫sin⁡(2x) dx\int\sin\left(2x\right)\ dx  

cos⁡(2x)+C\cos\left(2x\right)+C  

  −12cos⁡(2x)+C-\frac{1}{2}\cos\left(2x\right)+C  

−cos⁡(2x)+C-\cos\left(2x\right)+C  

12cos⁡(2x)+C\frac{1}{2}\cos\left(2x\right)+C  

5.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the antiderivative:

∫x(x2+5)7dx \int x\left(x^2+5\right)^7dx\  

(2x+5)88+c\frac{\left(2x+5\right)^8}{8}+c  

(x2+5)816+c\frac{\left(x^2+5\right)^8}{16}+c  

(x2+5)66+c\frac{\left(x^2+5\right)^6}{6}+c  

(2x+5)816+c\frac{\left(2x+5\right)^8}{16}+c  

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the antiderivative:

∫2x3+x2dx \int\frac{2x}{\sqrt{3+x^2}}dx\  

123+x2+C\frac{1}{2\sqrt{3+x^2}}+C  

3+x2+C\sqrt{3+x^2}+C  

23+x2+C2\sqrt{3+x^2}+C  

23+x3+C\frac{2}{\sqrt{3+x^3}}+C  

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the antiderivative:

∫4sec⁡2(4x)tan⁡(4x)​dx\int4\sec^2\left(4x\right)\tan\left(4x\right)​dx

2(tan⁡4x)32+C2\left(\tan4x\right)^{\frac{3}{2}}+C

154⋅(tan⁡4x)43+C\frac{15}{4}\cdot\left(\tan4x\right)^{\frac{4}{3}}+C

43⋅(tan⁡4x)32+C\frac{4}{3}\cdot\left(\tan4x\right)^{\frac{3}{2}}+C

23⋅(tan⁡4x)32+C\frac{2}{3}\cdot\left(\tan4x\right)^{\frac{3}{2}}+C

Tags

CCSS.HSF.TF.B.7

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