What is the integral of x^{-4}*ln(x) ?

The integral of x^{-4}*ln(x) is -(ln(x))/(3x^3)-1/(9x^3)+C

Popular >

integral of x^{-4}*ln(x)

\int x^{- 4} \cdot ln (x) d x

- \frac{ln ( x )}{3 x ^{3}} - \frac{1}{9 x ^{3}} + C

Solution steps

\int x^{- 4} ln (x) d x

Simplify

x^{- 4} ln (x) : \frac{ln ( x )}{x ^{4}}

= \int \frac{ln ( x )}{x ^{4}} d x

Apply Integration By Parts

: - \frac{ln ( x )}{3 x ^{3}} - \int - \frac{1}{3 x ^{4}} d x

= - \frac{ln ( x )}{3 x ^{3}} - \int - \frac{1}{3 x ^{4}} d x

\int - \frac{1}{3 x ^{4}} d x = \frac{1}{9 x ^{3}}

= - \frac{ln ( x )}{3 x ^{3}} - \frac{1}{9 x ^{3}}

Add a constant to the solution

= - \frac{ln ( x )}{3 x ^{3}} - \frac{1}{9 x ^{3}} + C

\int \frac{x}{12 - x ^{2}} d x

\int \frac{1}{v ^{2}} 1 + \frac{1}{v} d v

\int \frac{sin ^{2} ( y )}{tan ^{4} ( y )} d y

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

\int \frac{2 ( 1 + x )}{27} d x

What is the integral of x^{-4}*ln(x) ?
The integral of x^{-4}*ln(x) is -(ln(x))/(3x^3)-1/(9x^3)+C