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

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

\int x^{- 4} 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

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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