What is the integral of 1/((2x+5)^{11)} ?

The integral of 1/((2x+5)^{11)} is -1/(20(2x+5)^{10)}+C

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integral of 1/((2x+5)^{11)}

\int \frac{1}{( 2 x + 5 ) ^{11}} d x

- \frac{1}{20 ( 2 x + 5 ) ^{10}} + C

Solution steps

\int \frac{1}{( 2 x + 5 ) ^{11}} d x

Apply u-substitution

: \int \frac{1}{2 u ^{11}} d u

= \int \frac{1}{2 u ^{11}} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u ^{11}} d u

Apply the Power Rule

: - \frac{1}{10 u ^{10}}

= \frac{1}{2} (- \frac{1}{10 u ^{10}})

Substitute back

u = 2 x + 5

= \frac{1}{2} (- \frac{1}{10 ( 2 x + 5 ) ^{10}})

Simplify

\frac{1}{2} (- \frac{1}{10 ( 2 x + 5 ) ^{10}}) : - \frac{1}{20 ( 2 x + 5 ) ^{10}}

= - \frac{1}{20 ( 2 x + 5 ) ^{10}}

Add a constant to the solution

= - \frac{1}{20 ( 2 x + 5 ) ^{10}} + C

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What is the integral of 1/((2x+5)^{11)} ?
The integral of 1/((2x+5)^{11)} is -1/(20(2x+5)^{10)}+C