What am I doing wrong on this integration problem?
$ \begin{align*} \int\frac{t^3}{1+t^2} &= \frac14 t^4 (\ln(1+t^2) (t+\frac13 t^3)) \\ &= \frac14 t^4(t \ln(1+t^2)+\frac13 t^3 \ln(1+t^2) \\ &= \frac14 t^5 \ln(1+t^2)+\frac{1}{3}t^7 \ln(1+t^2) \end{align*}$
Answer should be $\frac{1}{2}(t^2-\ln(t^2+1))$. I'm way off
Any help appreciated. Thanks!