do it by using BY PARTS......
take tan inverse x as first funcn. & x as second function.....
its easy..

 

 

 u.v . dx = u  v .dx -  u' .(  v.dx .) dx

 

applying we get

 

x^4 /4tan-1 x  - 1/4  x^4 .dx

                             1 + x^2

 

add + 1 and -1 in integral we get d answer as

 

x^4 / 4 tan-1 x  - tan-1x /4  - 1/4(x^3 - x)--------------ans.

                                                 3