If you have gotten it to
to evaluate the next integral, let so that .
I want to integrate x*arcsinx. I let u = arcsinx and dv = x and proceed. When I get to the next step, I have an x^2 numerator and a sqrt(1-x^2) denominator and I am stuck. Could someone help me proceed from here? I used Wolfram Alpha to get an answer and still can't work it out. Thanks!
It just comes with experience, but generally if you have or somewhere in the denominator, the plan is to use an appropriate trigonometric or hyperbolic substitution, combined with some form of the Pythagorean Identity to simplify the denominator and to cancel with the derivative.