Evaluate ∫$$ex4$$−$$e2xdx$$

Correct option is 2sin−1⁡ex2+C

Questions

$Evaluate \int \frac{e^{x}}{\sqrt{4 - e^{2 x}}} d x$

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12sin−1⁡ex2+C

sin−1⁡ex2+C

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detailed solution

Correct option is B

I=∫ex4−e2xdx=∫ex22−ex2dx Let ex=t or exdx=dt∴ I=∫dt4−t2=∫dt22−t2 =sin−1⁡t2+C=sin−1⁡ex2+C

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Evaluate ∫ex4−e2xdx

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$Evaluate \int \frac{e^{x}}{\sqrt{4 - e^{2 x}}} d x$