What is int ((arcsinx)^9) / (sqrt(1-x^2) dx?

1 Answer
May 29, 2018

color(blue)[int ((arcsinx)^9) / (sqrt(1-x^2)] dx=(arcsinx)^10/10+c]

Explanation:

int ((arcsinx)^9) / (sqrt(1-x^2)] dx

lets suppose:

u=arcsinx

du=1/sqrt(1-x^2)*dx

dx=sqrt(1-x^2)*du

int ((arcsinx)^9) / (sqrt(1-x^2) dx]=int ((u)^9*sqrt(1-x^2))/ (sqrt(1-x^2)]*du

intu^9*du=u^10/10=(arcsinx)^10/10+c