What is the integral of ((-2+ln(-2x))^{-3})/x ?

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

Popular >

integral of ((-2+ln(-2x))^{-3})/x

\int \frac{( - 2 + ln ( - 2 x ) ) ^{- 3}}{x} d x

- \frac{1}{2 ( - 2 + ln ( - 2 x ) ) ^{2}} + C

Solution steps

\int \frac{( - 2 + ln ( - 2 x ) ) ^{- 3}}{x} d x

Apply u-substitution

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

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

Apply the Power Rule

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

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

Substitute back

u = - 2 + ln (- 2 x)

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

Add a constant to the solution

= - \frac{1}{2 ( - 2 + ln ( - 2 x ) ) ^{2}} + C

\int 6 (300 + x)^{2} d x

\int \frac{7 x + 1}{3 x ^{2} + 6 x} d x

\int \frac{x ^{2} cos ( x - 2 x ) sin ( x )}{x ^{4}} d x

\int \frac{2 x ^{5} + 3 x ^{2}}{2 x ^{3} + 1} d x

\int \frac{( 2 )}{3 + 2 x} d x

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