Integrate the following functions `xsqrt(1+2x^2)`

Explanation

Put `1+2x^2 = t`.
Then dt = 4x dx `gt xdx = 1/4 dt`
therefore `int x sqrt(1+2x^2) dx = int sqrtt 1/4 dt`
=`1/4 int sqrtt dt = 1/4 t^(1/2+1)/(1/2+1) +c`
=`1/6 t^(3/2) +c = 1/6 (1+2x^2)^(3/2) +c`