How to solve the following indefinite integral? $$ \int \frac{\lambda \alpha t^\alpha}{(1+\lambda t^{\alpha})^2}dt $$ where $\lambda,\alpha$ are real numbers.
I've tried to integration by part, however I came across $\int \frac{1}{1+\lambda t^\alpha}dt$, which I still couldn't solve.
So, can anybody give me a hint? Big thanks!