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)

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

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

e^{2 t} sin (5 t)

\frac{4 - 3 x - x ^{2}}{x ^{2} - 6}

\int_{0}^{\frac{π}{2}} - 2 sin^{2} (3 x) d x

(\frac{d y}{d x}) = 0.011 \cdot y \cdot (2 - (y - 25))

\int \frac{5}{( 3 x - 1 ) ^{7}} d x

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