What is the integral of (ln(x^2-16))/(x^2) ?

The integral of (ln(x^2-16))/(x^2) is -(ln(x^2-16))/x-1/4 (ln| x/4+1|-ln| x/4-1|)+C

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integral of (ln(x^2-16))/(x^2)

\int \frac{ln ( x ^{2} - 16 )}{x ^{2}} d x

- \frac{ln ( x ^{2} - 16 )}{x} - \frac{1}{4} (ln \frac{x}{4} + 1 - ln \frac{x}{4} - 1) + C

Solution steps

\int \frac{ln ( x ^{2} - 16 )}{x ^{2}} d x

Apply Integration By Parts

= - \frac{ln ( x ^{2} - 16 )}{x} - \int - \frac{2}{x ^{2} - 16} d x

\int - \frac{2}{x ^{2} - 16} d x = \frac{1}{4} (ln \frac{x}{4} + 1 - ln \frac{x}{4} - 1)

= - \frac{ln ( x ^{2} - 16 )}{x} - \frac{1}{4} (ln \frac{x}{4} + 1 - ln \frac{x}{4} - 1)

Add a constant to the solution

= - \frac{ln ( x ^{2} - 16 )}{x} - \frac{1}{4} (ln \frac{x}{4} + 1 - ln \frac{x}{4} - 1) + C

What is the integral of (ln(x^2-16))/(x^2) ?
The integral of (ln(x^2-16))/(x^2) is -(ln(x^2-16))/x-1/4 (ln| x/4+1|-ln| x/4-1|)+C