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

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

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integral of ln(x^2+2)

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

x ln (x^{2} + 2) + 22 arctan (\frac{x}{2}) - 2 x + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{2 x ^{2}}{x ^{2} + 2} d x = - 22 arctan (\frac{x}{2}) + 2 x

= x ln (x^{2} + 2) - (- 22 arctan (\frac{x}{2}) + 2 x)

Simplify

= x ln (x^{2} + 2) + 22 arctan (\frac{x}{2}) - 2 x

Add a constant to the solution

= x ln (x^{2} + 2) + 22 arctan (\frac{x}{2}) - 2 x + C

\int 17 sin^{2} (x co) s^{2} x d x

\int sin^{2} (3 t) d t

\int 5 sin (ln (x)) d x

f (x) = \frac{x}{x ^{2} + 36}

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