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Let  take  x^2 = u

Differentiate it both side we get

2x dx = du

dx = du/2x

plug the value of dx and x^2 we get

=

=…………….(1)

Now split the term using partial fraction we get

Multiply by (1+u)(u-2) We get

A(u-2) + B(1+u)  = 1  …………(2)

Plug u = 2 we get

3B= 1  

B = 1/3

Now plug u = -1 in equation (2) we get

-3A= 1

A = - 1/3

Plug the value back in equation first we get

=

Now use the formula of integration  we get

=

=  +c

=