Hier noch die Lösung von Wolframalpha, falls die Seite mal down ist
Take the integral:
integral sin(sqrt(x)) dx
For the integrand sin(sqrt(x)), substitute u = sqrt(x) and du = 1/(2 sqrt(x)) dx:
= 2 integral u sin(u) du
For the integrand u sin(u), integrate by parts, integral f dg = f g- integral g df, where f = u, dg = sin(u) du, df = du, g = -cos(u):
= 2 integral cos(u) du-2 u cos(u)
The integral of cos(u) is sin(u):
= 2 sin(u)-2 u cos(u)+constant
Substitute back for u = sqrt(x):
Answer:
= 2 sin(sqrt(x))-2 sqrt(x) cos(sqrt(x))+constant