INTEGRAL CALCULUS

Question

integral(1/(x^1/3+x^1/4)+log(1+x^1/6)/(x^1/3+x^1/2), dx)

Answer 1

Sumit,

 

Are you using a CAS program or calculator for this, or must it be done by written computation only?

 

If the answer is the latter, I recommend looking at all of the powers of x which appear in the integrand:

 

1/3, 1/4, and 1/6.

 

The LCD of these three fractions is 12, so I would recommend (just to get started) using the substitution u = x^1/12.

 

You then have x^1/3 = u⁴, x^1/4 = u³, and x^1/6 = u², with du = 1/12 x^-11/12 dx.

 

This may or may not prove helpful, but it is at least an idea to get you started. One question. If you are not using a CAS program, is log to the base 10 or e?

 

Let me know if this helps you or if you need additional insight or hints.