What is the integral of (8x+5)^{-3} ?

The integral of (8x+5)^{-3} is -1/(16(8x+5)^2)+C

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integral of (8x+5)^{-3}

\int (8 x + 5)^{- 3} d x

- \frac{1}{16 ( 8 x + 5 ) ^{2}} + C

Solution steps

\int (8 x + 5)^{- 3} d x

Apply exponent rule:

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

= \int \frac{1}{( 8 x + 5 ) ^{3}} d x

Apply u-substitution

: \int \frac{1}{8 u ^{3}} d u

= \int \frac{1}{8 u ^{3}} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int \frac{1}{u ^{3}} d u

Apply the Power Rule

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

= \frac{1}{8} (- \frac{1}{2 u ^{2}})

Substitute back

u = 8 x + 5

= \frac{1}{8} (- \frac{1}{2 ( 8 x + 5 ) ^{2}})

Simplify

\frac{1}{8} (- \frac{1}{2 ( 8 x + 5 ) ^{2}}) : - \frac{1}{16 ( 8 x + 5 ) ^{2}}

= - \frac{1}{16 ( 8 x + 5 ) ^{2}}

Add a constant to the solution

= - \frac{1}{16 ( 8 x + 5 ) ^{2}} + C

\frac{d}{d x} ((8 x^{2} - 13 x) e^{x})

\int_{0}^{- 1} (- 16 3 x) d x

x \to - 1 lim (\frac{x ^{2} - 7}{1 - x})

f (x) = ln (ln (x))

\int e^{- 0.02 t} (e^{- 0.13 t} + 4) d t

What is the integral of (8x+5)^{-3} ?
The integral of (8x+5)^{-3} is -1/(16(8x+5)^2)+C