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

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

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integral of ln(1+y^2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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