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Question Number 43156 by MASANJA J last updated on 07/Sep/18

integrate w.r.t x  ∫((xe^x )/(√(1+x^2 )))dx

$${integrate}\:{w}.{r}.{t}\:{x} \\ $$$$\int\frac{{xe}^{{x}} }{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 09/Sep/18

x=tanα  dx=sec^2 αdα  ∫((tanα.e^(tanα) .sec^2 α)/(secα))dα  ∫e^(tanα) (tanαsecα)dα  ∫e^(tanα) d(secα)  contd...

$${x}={tan}\alpha\:\:{dx}={sec}^{\mathrm{2}} \alpha{d}\alpha \\ $$$$\int\frac{{tan}\alpha.{e}^{{tan}\alpha} .{sec}^{\mathrm{2}} \alpha}{{sec}\alpha}{d}\alpha \\ $$$$\int{e}^{{tan}\alpha} \left({tan}\alpha{sec}\alpha\right){d}\alpha \\ $$$$\int{e}^{{tan}\alpha} {d}\left({sec}\alpha\right) \\ $$$${contd}... \\ $$$$ \\ $$

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