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

The integral of ln(y^2+1) is yln(y^2+1)-2(-arctan(y)+y)+C

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integral of ln(y^2+1)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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