# Integration over time by having derivation

Assume we want to find the following integration:

$$\int_{t=0}^{\infty} p(t)dt$$

where $p(0)=p$ and also $$\frac{dp(t)}{dt}=-p(t)(1-p(t))\mu$$.

Is there any easy way to exploit the second equation and calculate the first integration?

Any comment is highly appreciated.

• – Git Gud Apr 21 '14 at 21:14
• You have the ODE $\dot p=\mu p(p-1)$, thus $p=\frac{\dot p}{\mu(p-1)}$. – David H Apr 21 '14 at 21:18