What is the integral of 8/((8x+5)^6) ?

The integral of 8/((8x+5)^6) is -1/(5(8x+5)^5)+C

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integral of 8/((8x+5)^6)

\int \frac{8}{( 8 x + 5 ) ^{6}} d x

- \frac{1}{5 ( 8 x + 5 ) ^{5}} + C

Solution steps

\int \frac{8}{( 8 x + 5 ) ^{6}} d x

Take the constant out:

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

= 8 \cdot \int \frac{1}{( 8 x + 5 ) ^{6}} d x

Apply u-substitution

= 8 \cdot \int \frac{1}{8 u ^{6}} d u

Take the constant out:

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

= 8 \cdot \frac{1}{8} \cdot \int \frac{1}{u ^{6}} d u

Apply the Power Rule

= 8 \cdot \frac{1}{8} (- \frac{1}{5 u ^{5}})

Substitute back

u = 8 x + 5

= 8 \cdot \frac{1}{8} (- \frac{1}{5 ( 8 x + 5 ) ^{5}})

Simplify

8 \cdot \frac{1}{8} (- \frac{1}{5 ( 8 x + 5 ) ^{5}}) : - \frac{1}{5 ( 8 x + 5 ) ^{5}}

= - \frac{1}{5 ( 8 x + 5 ) ^{5}}

Add a constant to the solution

= - \frac{1}{5 ( 8 x + 5 ) ^{5}} + C

What is the integral of 8/((8x+5)^6) ?
The integral of 8/((8x+5)^6) is -1/(5(8x+5)^5)+C