Evaluate The Integral...

Question

Evaluate The Integral

Answer 1

Firstly, we can rewrite the integral as ∫(arccos(x))¹⁰/√(1-x²) dx for simplicity (note that arccos(x)=cos^-1(x)).

Let u=arccos(x) and du=-1/√(1-x²)dx so that -du=1/√(1-x²)dx:

-∫u¹⁰du

= -u¹¹/11 + C

= -(arccos(x))¹¹/11 + C

= -(cos^-1(x))¹¹/11 + C

Hope this helped! It's good to know your trig inverse derivatives for problems like these!