Question

Integration by Parts
∫ tan^-1(y)dy

Answer 1

\[\int\limits_{}^{} udv = uv - \int\limits_{}^{} vdu\]
\[u = \tan^{-1}(y)\]\[du = \frac{ 1 }{ 1 + y^2 }\]\[dv = dy\]\[v = y\]

plug and play. it will require a second, simpler integration

Answer 2

small correction:
\[du = \frac{ 1 }{ 1 + y^2 } dy\]***