Evaluate: e^ x 5 - 4c^ X - e^ 2_ x dx - Vidyadip

Question

$\text{Evaluate:} \int \frac{e^{x}}{\sqrt{5 - 4c^{X} - e^{2_{x}}}} \text{dx}$

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Answer

$\text{Getting I} = \int\frac{dt}{\sqrt{5 - 4t - t^{2}}} \text{where t = e}^{x}$

$= \int\frac{dt}{\sqrt{(3)^{2}} - ( t + 2)^{2}}$

$= \sin^{-1} \frac{t + 2}{3} + c$

$= \sin^{-1} \frac{e^{x} + 2}{3} + c$

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