If y = a x n ax^n a x n , then ∫ y d x = \int_{ }^{ }y\ dx\ = ∫ y d x =

a x n + 1 n + 1 + c \frac{ax^{n+1}}{n+1}+\ c n + 1 a x n + 1 + c

a x n + 1 n + 1 \frac{ax^{n+1}}{n+1} n + 1 a x n + 1

a x n − 1 n − 1 + c \frac{ax^{n-1}}{n-1}+\ c n − 1 a x n − 1 + c

a x n + 1 n + c \frac{ax^{n+1}}{n}+\ c n a x n + 1 + c

Integrate x \sqrt{x} x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> with respect to x

2 3 x 3 2 + c \frac{2}{3}x^{\frac{3}{2}}+\ c 3 2 x 2 3 + c

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

1 2 x − 1 2 + c \frac{1}{2}x^{-\frac{1}{2}}+\ c 2 1 x − 2 1 + c

3 2 x 3 2 + c \frac{3}{2}x^{\frac{3}{2}}+\ c 2 3 x 2 3 + c

Integrate ∫ ( 2 x + 1 ) 10 d x \int\left(2x+1\right)^{10}\ dx ∫ ( 2 x + 1 ) 1 0 d x with respect to x.

1 22 ( 2 x + 1 ) 11 + c \frac{1}{22}\left(2x+1\right)^{11}+c 2 2 1 ( 2 x + 1 ) 1 1 + c

22 ( 2 x + 1 ) 11 + c 22\left(2x+1\right)^{11}+c 2 2 ( 2 x + 1 ) 1 1 + c

11 ( 2 x + 1 ) 10 + c 11\left(2x+1\right)^{10}+c 1 1 ( 2 x + 1 ) 1 0 + c

1 11 ( 2 x + 1 ) 10 + c \frac{1}{11}\left(2x+1\right)^{10}+c 1 1 1 ( 2 x + 1 ) 1 0 + c

Integrate sin ⁡ ( x 2 ) \sin\left(\frac{x}{2}\right) sin ( 2 x ) with respect to x

− 2 cos ⁡ ( x 2 ) + c -2\cos\left(\frac{x}{2}\right)\ +\ c − 2 cos ( 2 x ) + c

cos ⁡ ( x 2 ) + c \cos\left(\frac{x}{2}\right)\ +\ c cos ( 2 x ) + c

− cos ⁡ ( x 2 ) + c -\cos\left(\frac{x}{2}\right)\ +\ c − cos ( 2 x ) + c

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

Find indefinite integral for ∫ 1 e 5 x d x \int_{ }^{ }\frac{1}{e^{5x}}\ dx ∫ e 5 x 1 d x

e − 5 x − 5 + c \frac{e^{-5x}}{-5}+\ c − 5 e − 5 x + c

1 5 e 5 x + c \frac{1}{5}e^{5x}\ +\ c 5 1 e 5 x + c

− 5 e 4 x + c -5e^{4x}\ +\ c − 5 e 4 x + c

e − 4 x − 4 + c \frac{e^{-4x}}{-4}+\ c − 4 e − 4 x + c

Basic Integration

Authored by Izni Rais

Mathematics

University

CCSS covered

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If y = $ax^n$ , then $\int_{ }^{ }y\ dx\ =$

$\frac{ax^{n+1}}{n+1}$

$\frac{ax^{n-1}}{n-1}+\ c$

$\frac{ax^{n+1}}{n}+\ c$

$\frac{ax^{n+1}}{n+1}+\ c$

Tags

CCSS.HSA.APR.A.1

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is the indefinite integral of $\frac{x^3}{2}+7$ ?

$\frac{3x^2}{2}$

$\frac{3x^2}{2}+7x+c$

$\frac{x^4}{8}+7x+c$

$\frac{x^4}{8}+c$

Tags

CCSS.HSA.APR.A.1

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

Integrate $\sqrt{x}$ with respect to x

$x^{\frac{1}{2}}+c$

$\frac{1}{2}x^{-\frac{1}{2}}+\ c$

$\frac{2}{3}x^{\frac{3}{2}}+\ c$

$\frac{3}{2}x^{\frac{3}{2}}+\ c$

Tags

CCSS.HSN.RN.A.2

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

Which of the following is the indefinite integral of $\frac{3}{x^4}\ \ ?$

$-\frac{1}{x^3}+\ c$

$\frac{3}{5x^5}+\ c$

$-\frac{12}{x^5}+\ c$

$\frac{1}{x^3}+\ c$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Integrate $\int\left(2x+1\right)^{10}\ dx$ with respect to x.

$22\left(2x+1\right)^{11}+c$

$\frac{1}{22}\left(2x+1\right)^{11}+c$

$11\left(2x+1\right)^{10}+c$

$\frac{1}{11}\left(2x+1\right)^{10}+c$

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

$\int_{ }^{ }\ \frac{1}{x}+\ \frac{1}{x^2}\ dx$

$x^{-1}\ +\ x^{-2}+\ c$

$x^0\ -\ x^{-1}+\ c$

$\ln x+\ x^{-1}+\ c$

$\ln x-\ x^{-1}+\ c$

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\int_{ }^{ }\sec^2\ 5x\ \ dx\ \ =$

$\tan\ x\ \ +\ c$

$\frac{1}{5}\tan\ x\ \ +\ c$

$\frac{1}{5}\tan\ 5x\ \ +\ c$

$\frac{1}{5}\tan^2\ 5x\ \ +\ c$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Integrate $\sin\left(\frac{x}{2}\right)$ with respect to x

$\cos\left(\frac{x}{2}\right)\ +\ c$

$-2\cos\left(\frac{x}{2}\right)\ +\ c$

$-\cos\left(\frac{x}{2}\right)\ +\ c$

$-\frac{1}{2}\cos\left(\frac{x}{2}\right)\ +\ c$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

Find the integral with respect to x of $\int_{ }^{ }\ \left(e^{3x}\right)^2\ dx\ .$

$\frac{e^{6x}}{6}\ +\ c$

$\frac{e^{9x}}{9}\ +\ c$

$6e^{6x}\ +\ c$

$\left(e^{3x}\right)^2\ +\ c$

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find indefinite integral for $\int_{ }^{ }\frac{1}{e^{5x}}\ dx$

$\frac{1}{5}e^{5x}\ +\ c$

$-5e^{4x}\ +\ c$

$\frac{e^{-5x}}{-5}+\ c$

$\frac{e^{-4x}}{-4}+\ c$

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Basic Integration

If y = axnax^naxn , then ∫y dx =\int_{ }^{ }y\ dx\ =∫​y dx =

Which of the following is the indefinite integral of x32+7\frac{x^3}{2}+72x3​+7 ?

Integrate x\sqrt{x}x​ with respect to x

Which of the following is the indefinite integral of 3x4 ?\frac{3}{x^4}\ \ ?x43​ ?

Integrate ∫(2x+1)10 dx\int\left(2x+1\right)^{10}\ dx∫(2x+1)10 dx with respect to x.

∫ 1x+ 1x2 dx\int_{ }^{ }\ \frac{1}{x}+\ \frac{1}{x^2}\ dx∫​ x1​+ x21​ dx

∫sec⁡2 5x dx =\int_{ }^{ }\sec^2\ 5x\ \ dx\ \ =∫​sec2 5x dx =

Integrate sin⁡(x2)\sin\left(\frac{x}{2}\right)sin(2x​) with respect to x

Find the integral with respect to x of ∫ (e3x)2 dx .\int_{ }^{ }\ \left(e^{3x}\right)^2\ dx\ .∫​ (e3x)2 dx .

Find indefinite integral for ∫1e5x dx\int_{ }^{ }\frac{1}{e^{5x}}\ dx∫​e5x1​ dx

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Discover more resources for Mathematics

If y = $ax^n$ , then $\int_{ }^{ }y\ dx\ =$

Which of the following is the indefinite integral of $\frac{x^3}{2}+7$ ?

Integrate $\sqrt{x}$ with respect to x

Which of the following is the indefinite integral of $\frac{3}{x^4}\ \ ?$

Integrate $\int\left(2x+1\right)^{10}\ dx$ with respect to x.

$\int_{ }^{ }\ \frac{1}{x}+\ \frac{1}{x^2}\ dx$

$\int_{ }^{ }\sec^2\ 5x\ \ dx\ \ =$

Integrate $\sin\left(\frac{x}{2}\right)$ with respect to x

Find the integral with respect to x of $\int_{ }^{ }\ \left(e^{3x}\right)^2\ dx\ .$

Find indefinite integral for $\int_{ }^{ }\frac{1}{e^{5x}}\ dx$