What is the integral of (54)/((9x+5)^7) ?

The integral of (54)/((9x+5)^7) is -1/((9x+5)^6)+C

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integral of (54)/((9x+5)^7)

\int \frac{54}{( 9 x + 5 ) ^{7}} d x

- \frac{1}{( 9 x + 5 ) ^{6}} + C

Solution steps

\int \frac{54}{( 9 x + 5 ) ^{7}} d x

Take the constant out:

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

= 54 \cdot \int \frac{1}{( 9 x + 5 ) ^{7}} d x

Apply u-substitution

: \int \frac{1}{9 u ^{7}} d u

= 54 \cdot \int \frac{1}{9 u ^{7}} d u

Take the constant out:

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

= 54 \cdot \frac{1}{9} \cdot \int \frac{1}{u ^{7}} d u

Apply the Power Rule

: - \frac{1}{6 u ^{6}}

= 54 \cdot \frac{1}{9} (- \frac{1}{6 u ^{6}})

Substitute back

u = 9 x + 5

= 54 \cdot \frac{1}{9} (- \frac{1}{6 ( 9 x + 5 ) ^{6}})

Simplify

54 \cdot \frac{1}{9} (- \frac{1}{6 ( 9 x + 5 ) ^{6}}) : - \frac{1}{( 9 x + 5 ) ^{6}}

= - \frac{1}{( 9 x + 5 ) ^{6}}

Add a constant to the solution

= - \frac{1}{( 9 x + 5 ) ^{6}} + C

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What is the integral of (54)/((9x+5)^7) ?
The integral of (54)/((9x+5)^7) is -1/((9x+5)^6)+C