Can someone please show all the steps of how the answers on

Can someone please show all the steps of how the answers on the right were obtained from the integrals on the left?

Solution

Here in all the problems, factorization is done.

I will tell u for 1st prolem.

Here we can write denominator as :

2x^3+x^2-x

= x(2x^2+x-1)

x(2x-1)(x+1)

So, we get

1 = A/(x) + B/(2x-1) + C/(x+1)

A=-1, B = 2/3,c=1/3