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

The integral of x^{-3}ln(5x) is -(ln(5x))/(2x^2)-1/(4x^2)+C

integral of x^{-3}ln(5x)

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

- \frac{ln ( 5 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C

Solution steps

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

Simplify

x^{- 3} ln (5 x) : \frac{ln ( 5 x )}{x ^{3}}

= \int \frac{ln ( 5 x )}{x ^{3}} d x

Apply Integration By Parts

= - \frac{ln ( 5 x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x

\int - \frac{1}{2 x ^{3}} d x = \frac{1}{4 x ^{2}}

= - \frac{ln ( 5 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}

Add a constant to the solution

= - \frac{ln ( 5 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C

n = 6 \sum \infty e^{5 - 2 n}

\frac{d}{d x} (\frac{e ^{x} + 1}{e ^{x} - 1})

d er i v a t i v e f (x) = 9 x^{8} e^{x} + e^{x} x^{9}

\int_{0}^{1} x^{2} ln (x) d x

\int_{0}^{N} e^{- s t} e^{- 3 t} d t

What is the integral of x^{-3}ln(5x) ?
The integral of x^{-3}ln(5x) is -(ln(5x))/(2x^2)-1/(4x^2)+C