What is the integral of (ln(x))/(x^{13)} ?

The integral of (ln(x))/(x^{13)} is -(ln(x))/(12x^{12)}-1/(144x^{12)}+C

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integral of (ln(x))/(x^{13)}

\int \frac{ln ( x )}{x ^{13}} d x

- \frac{ln ( x )}{12 x ^{12}} - \frac{1}{144 x ^{12}} + C

Solution steps

\int \frac{ln ( x )}{x ^{13}} d x

Apply Integration By Parts

: - \frac{ln ( x )}{12 x ^{12}} - \int - \frac{1}{12 x ^{13}} d x

= - \frac{ln ( x )}{12 x ^{12}} - \int - \frac{1}{12 x ^{13}} d x

\int - \frac{1}{12 x ^{13}} d x = \frac{1}{144 x ^{12}}

= - \frac{ln ( x )}{12 x ^{12}} - \frac{1}{144 x ^{12}}

Add a constant to the solution

= - \frac{ln ( x )}{12 x ^{12}} - \frac{1}{144 x ^{12}} + C

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What is the integral of (ln(x))/(x^{13)} ?
The integral of (ln(x))/(x^{13)} is -(ln(x))/(12x^{12)}-1/(144x^{12)}+C