Question Number 81115 by Ak5060 last updated on 09/Feb/20
![e^x ∫((2csec^2 θ dθ)/([4+(2tanθ)^2 ]^(3/2) )) = e^x ∫((2csec^2 θ dθ)/([4+(2tanθ)^2 ]^(3/2) )) =](https://www.tinkutara.com/question/Q81115.png)
$$\mathrm{e}^{\mathrm{x}} \int\frac{\mathrm{2}{csec}^{\mathrm{2}} \theta\:{d}\theta}{\left[\mathrm{4}+\left(\mathrm{2}{tan}\theta\right)^{\mathrm{2}} \right]^{\mathrm{3}/\mathrm{2}} }\:\:= \\ $$$$\mathrm{e}^{\mathrm{x}} \int\frac{\mathrm{2}{csec}^{\mathrm{2}} \theta\:{d}\theta}{\left[\mathrm{4}+\left(\mathrm{2}{tan}\theta\right)^{\mathrm{2}} \right]^{\mathrm{3}/\mathrm{2}} }\:\:= \\ $$