What is the integral of ln(x^2+8) ?

The integral of ln(x^2+8) is xln(x^2+8)+4sqrt(2)arctan(x/(2sqrt(2)))-2x+C

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integral of ln(x^2+8)

\int ln (x^{2} + 8) d x

x ln (x^{2} + 8) + 42 arctan (\frac{x}{2 2}) - 2 x + C

Solution steps

\int ln (x^{2} + 8) d x

Apply Integration By Parts

: x ln (x^{2} + 8) - \int \frac{2 x ^{2}}{x ^{2} + 8} d x

= x ln (x^{2} + 8) - \int \frac{2 x ^{2}}{x ^{2} + 8} d x

\int \frac{2 x ^{2}}{x ^{2} + 8} d x = - 42 arctan (\frac{x}{2 2}) + 2 x

= x ln (x^{2} + 8) - (- 42 arctan (\frac{x}{2 2}) + 2 x)

Simplify

= x ln (x^{2} + 8) + 42 arctan (\frac{x}{2 2}) - 2 x

Add a constant to the solution

= x ln (x^{2} + 8) + 42 arctan (\frac{x}{2 2}) - 2 x + C

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What is the integral of ln(x^2+8) ?
The integral of ln(x^2+8) is xln(x^2+8)+4sqrt(2)arctan(x/(2sqrt(2)))-2x+C