Step by step of evaluating the integral.

Question

Evaluate the integral (x⁴+X²+4 all over x⁶+4x⁴+4x²) dx.

Evaluate the integral cosh^-1 x dx.

Help please!!

Answer 1

I will not solve these for you but I will tell you how to do them.

For inverse cosh: integrate by parts with u=cosh^-1x, du=1/sqrt(x²-1), v=x, dv=1

The integral you get will need the substitution=t=x²-1.

For the rational fraction: you will need partial fractions with denominators x², x²+2 and (x²+2)²

^{The first term is easy, the second term is an arcsin, and the third terms is integrable but messy (look it up in a short table)}