What is the integral of ln(1+1/(x^2)) ?

The integral of ln(1+1/(x^2)) is xln(1+1/(x^2))+2arctan(x)+C

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integral of ln(1+1/(x^2))

\int ln (1 + \frac{1}{x ^{2}}) d x

x ln (1 + \frac{1}{x ^{2}}) + 2 arctan (x) + C

Solution steps

\int ln (1 + \frac{1}{x ^{2}}) d x

Apply Integration By Parts

: x ln (1 + \frac{1}{x ^{2}}) - \int - \frac{2}{x ^{2} + 1} d x

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

\int - \frac{2}{x ^{2} + 1} d x = - 2 arctan (x)

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

Simplify

= x ln (1 + \frac{1}{x ^{2}}) + 2 arctan (x)

Add a constant to the solution

= x ln (1 + \frac{1}{x ^{2}}) + 2 arctan (x) + C

\int (3 x + 1)^{\frac{1}{2}} d x

\frac{d}{d x} ((3 - 2 x)^{2})

f (x) = \frac{2 x}{x ^{2} + 1}, (- 1, - 1)

\frac{2 ( x + 1 )}{x ^{2} + 1}

r^{2} - 9 x^{2}

What is the integral of ln(1+1/(x^2)) ?
The integral of ln(1+1/(x^2)) is xln(1+1/(x^2))+2arctan(x)+C