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Question

Evaluate:
x31+x2dx

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Solution

Let I=x31+x2dx.

I=x2x1+x2dx

Put 1+x2=u, then,

x2=u1

2xdx=du

I=12u1udu

=12uudu121udu

=12udu121udu

=12(23u3/2)12(2u1/2)+c

=13u3/2u1/2+c

=u1/2(13u1)+c

=1+x2(1+x231)+c

=1+x2(1+x233)+c

=1+x2(x223)+c

=1+x23(x22)+c


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