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

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

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integral of ln(x^2+1)

integral

ln (x^{2} + 1)

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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

\frac{cos ^{2} ( x )}{sin ( x )}

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

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

\frac{e ^{x}}{x ^{2}}

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