**Evaluate**

**Solution.** It is clear by looking at the
given integral, that the major problem will be to handle and
. Indeed, it is always harder to handle the nth-root
functions when it comes to integration. Therefore a good substitution
will be to take care of both root-functions at the same time. For
example, we may choose which will make
and polynomial functions of *u*. For example, one
may take *n* = 36 which will give

Clearly we are generating a rational function of *u* which will take a
lot of work to handle. This leads us to reconsider the choice of *n*
and try to make it as small as possible. The right choice will be
*n*=6 which the least common factor of 2 and 3. In this case we have

The method of partial fractions gives

which gives

Hence we get

**
**

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Contact us

Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA

users online during the last hour