IXL - Find indefinite integrals using substitution (Calculus practice)

Find the indefinite integral. Use

to represent an arbitrary constant.

∫

cos

sin

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Learn with an example

question

Find the indefinite integral. Use

to represent an arbitrary constant.

∫

(

)

(

)

100

key idea

The substitution rule for indefinite integrals says that if

(

)

is a differentiable function whose range is an interval

and

(

)

is continuous on

then

∫

(

)

′

(

)

∫

(

)

solution

To find the indefinite integral of

(

)

(

)

100

use substitution.

The integrand contains

and its derivative,

This suggests that we let

and then

(

)

Substitute

and

(

)

into the integral, then integrate in terms of

∫

(

)

(

)

100

∫

(

)

100

(

)

∫

100

101

Finally, rewrite the answer in terms of

by substituting

101

(

)

101

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