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  • Find the integral of <img alt="\frac{e^{sin^{-1}x}}{\sqrt{1-x^{2}}}dx" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cfrac%7Be%5E%7Bsin%5E%7B-1%7Dx%7D%7D%7B%5Csqrt%7B1-x%5E%7B

Find the integral of \frac{e^{sin^{-1}x}}{\sqrt{1-x^{2}}}dx

Option: 1

-e^{sin^{-1}x}+C


Option: 2

e^{sin^{-1}x}+C


Option: 3

e^{sin^{-1}x}+C


Option: 4

e^{sin\ x}+C


Answers (1)

best_answer

Given integral,
\int\frac{e^{sin^{-1}x}}{\sqrt{1-x^{2}}}dx
Using the substitution method,
Let t = sin^{-1}x
Then,
\frac{1}{\sqrt{1-x^{2}}}dx=dt

Substituting the values in the given integral,
\int\frac{e^{sin^{-1}x}}{\sqrt{1-x^{2}}}dx=\int e^{t}dt
\int\frac{e^{sin^{-1}x}}{\sqrt{1-x^{2}}}dx=e^{t}+C
\int\frac{e^{sin^{-1}x}}{\sqrt{1-x^{2}}}dx=e^{sin^{-1}x}+C

 

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Nehul

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