Problem 76AE

Deriving formulas

Evaluate the following integrals. Assume a and b are real numbers and n is an integer.

∫ xn sin−1 x dx;Use integration by parts.

Answer

We have to evaluate the integral

∫

∫ =n ∫ (Take a constant out) ….(1)

Apply integration by parts

….(2)

Now put u=

∫ ]

∫ ] ……(3)

Now we evaluate the integral separately

Put

Substitute back we get

Put this value in equation (3) we get

∫

Therefore

∫

Where C is integration constant