What is the integral of (11x-7)^{-3} ?

The integral of (11x-7)^{-3} is -1/(22(11x-7)^2)+C

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integral of (11x-7)^{-3}

\int (11 x - 7)^{- 3} d x

- \frac{1}{22 ( 11 x - 7 ) ^{2}} + C

Solution steps

\int (11 x - 7)^{- 3} d x

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \int \frac{1}{( 11 x - 7 ) ^{3}} d x

Apply u-substitution

: \int \frac{1}{11 u ^{3}} d u

= \int \frac{1}{11 u ^{3}} d u

Take the constant out:

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

= \frac{1}{11} \cdot \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= \frac{1}{11} (- \frac{1}{2 u ^{2}})

Substitute back

u = 11 x - 7

= \frac{1}{11} (- \frac{1}{2 ( 11 x - 7 ) ^{2}})

Simplify

\frac{1}{11} (- \frac{1}{2 ( 11 x - 7 ) ^{2}}) : - \frac{1}{22 ( 11 x - 7 ) ^{2}}

= - \frac{1}{22 ( 11 x - 7 ) ^{2}}

Add a constant to the solution

= - \frac{1}{22 ( 11 x - 7 ) ^{2}} + C

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What is the integral of (11x-7)^{-3} ?
The integral of (11x-7)^{-3} is -1/(22(11x-7)^2)+C