What is the integral of 1/((2-x)^{13)} ?

The integral of 1/((2-x)^{13)} is 1/(12(2-x)^{12)}+C

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integral of 1/((2-x)^{13)}

\int \frac{1}{( 2 - x ) ^{13}} d x

\frac{1}{12 ( 2 - x ) ^{12}} + C

Solution steps

\int \frac{1}{( 2 - x ) ^{13}} d x

Apply u-substitution

: \int - \frac{1}{u ^{13}} d u

= \int - \frac{1}{u ^{13}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{u ^{13}} d u

Apply the Power Rule

: - \frac{1}{12 u ^{12}}

= - (- \frac{1}{12 u ^{12}})

Substitute back

u = 2 - x

= - (- \frac{1}{12 ( 2 - x ) ^{12}})

Simplify

= \frac{1}{12 ( 2 - x ) ^{12}}

Add a constant to the solution

= \frac{1}{12 ( 2 - x ) ^{12}} + C

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What is the integral of 1/((2-x)^{13)} ?
The integral of 1/((2-x)^{13)} is 1/(12(2-x)^{12)}+C