Integral of (e^(arcsinx))arcsinx dx
The solution
The answer (Indefinite)
[src]
/ ________
| asin(x) asin(x) / 2 asin(x)
| asin(x) x*e x*asin(x)*e \/ 1 - x *asin(x)*e
| E *asin(x) dx = C - ---------- + ------------------ + ----------------------------
| 2 2 2
/
$$\int e^{\operatorname{asin}{\left(x \right)}} \operatorname{asin}{\left(x \right)}\, dx = C + \frac{x e^{\operatorname{asin}{\left(x \right)}} \operatorname{asin}{\left(x \right)}}{2} - \frac{x e^{\operatorname{asin}{\left(x \right)}}}{2} + \frac{\sqrt{1 - x^{2}} e^{\operatorname{asin}{\left(x \right)}} \operatorname{asin}{\left(x \right)}}{2}$$
pi pi
-- --
2 2
e pi*e
- --- + ------
2 4
$$- \frac{e^{\frac{\pi}{2}}}{2} + \frac{\pi e^{\frac{\pi}{2}}}{4}$$
=
pi pi
-- --
2 2
e pi*e
- --- + ------
2 4
$$- \frac{e^{\frac{\pi}{2}}}{2} + \frac{\pi e^{\frac{\pi}{2}}}{4}$$
-exp(pi/2)/2 + pi*exp(pi/2)/4
Use the examples entering the upper and lower limits of integration.