What is the integral of e^{cos(arcsin(x))} ?

The integral of e^{cos(arcsin(x))} is e^{sqrt(1-x^2)}v+C

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integral of e^{cos(arcsin(x))}

\int e^{c o s (a r c s i n (x))} d v

e^{1 - x^{2}} v + C

Solution steps

\int e^{c o s (a r c s i n (x))} d v

Integral of a constant:

\int a d x = a x

= e^{c o s (a r c s i n (x))} v

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

= e^{1 - x^{2}} v

Add a constant to the solution

= e^{1 - x^{2}} v + C

What is the integral of e^{cos(arcsin(x))} ?
The integral of e^{cos(arcsin(x))} is e^{sqrt(1-x^2)}v+C