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

The integral of ln(t^2+1) is tln(t^2+1)-2(-arctan(t)+t)+C

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integral of ln(t^2+1)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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