**Find **

**Solution.** It is clear that once we develop
the through the binomial formula, we will get a
polynomial function easy to integrate. But it is clear that this will
take a lot of time with big possibility of doing mistakes !!

Let us consider the substitution (the reason behind is
the presence of *x* in the integral since the derivative of
is 2*x*). Indeed, we have *du* = 2*x dx* and therefore

We may check that the new integral is easier to handle since . Hence

which does not complete the answer since the indefinite integral
is a function of *x* not of
*u*. Therefore, we have to go back and replace *u* by *u*(*x*):

**
**

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