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

The integral of e^{arccos(x)} is 1/2 e^{arccos(x)}x-1/2 e^{arccos(x)}sqrt(-x^2+1)+C

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integral of e^{arccos(x)}

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

\frac{1}{2} e^{a r c c o s (x)} x - \frac{1}{2} e^{a r c c o s (x)} - x^{2} + 1 + C

Solution steps

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

Apply Integration By Parts

: e^{a r c c o s (x)} x - \int - \frac{e ^{a r c c o s (x)} x}{1 - x ^{2}} d x

= e^{a r c c o s (x)} x - \int - \frac{e ^{a r c c o s (x)} x}{1 - x ^{2}} d x

\int - \frac{e ^{a r c c o s (x)} x}{1 - x ^{2}} d x = - (- \frac{1}{2} e^{a r c c o s (x)} 1 - x^{2} - \frac{1}{2} e^{a r c c o s (x)} x)

= e^{a r c c o s (x)} x - (- (- \frac{1}{2} e^{a r c c o s (x)} 1 - x^{2} - \frac{1}{2} e^{a r c c o s (x)} x))

Simplify

e^{a r c c o s (x)} x - (- (- \frac{1}{2} e^{a r c c o s (x)} 1 - x^{2} - \frac{1}{2} e^{a r c c o s (x)} x)) : \frac{1}{2} e^{a r c c o s (x)} x - \frac{1}{2} e^{a r c c o s (x)} - x^{2} + 1

= \frac{1}{2} e^{a r c c o s (x)} x - \frac{1}{2} e^{a r c c o s (x)} - x^{2} + 1

Add a constant to the solution

= \frac{1}{2} e^{a r c c o s (x)} x - \frac{1}{2} e^{a r c c o s (x)} - x^{2} + 1 + C

\int 2 x - \frac{1}{x ^{2}} d x

\int 2^{x} + x^{2} d x

\frac{\partial}{\partial z} (yz - ln (x + z))

x \to - \infty lim (7)

\frac{d}{d x} (\frac{x ^{3}}{2 - x ^{2}})

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