1.

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

Answer»

Solution :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`


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