How to Solve integration by Using Dimensional analysis?

Question

H.C.Verma part 1 ...He suggested to solve it by Dimensional analysis but how i don't know.but by common mathod it is solve.

Answer 1

Integration by using Dimensional Analysis can only be used for partial checking of integration. It will not give you the full answer.

Take For example, consider the definite integral (and we will focus exclusively on definite integrals here)

integration ∫0ax5dx (1)
If we consider x to have dimension of length, then the integrand has units of length5 but you have to include another power of length from dx, so the final answer must have units of length6. The only nontrivial dimensionful constant in the problem is a, so the final answer must be proportional to a6; the right answer, of course, is a6/6.