JEE Advance - Mathematics (1992 - No. 20)
Find the indefinite integral $$\int {\left( {{1 \over {\root 3 \of x + \root 4 \of 4 }} + {{In\left( {1 + \root 6 \of x } \right)} \over {\root 3 \of x + \root \, \of x }}} \right)} dx$$
This integral requires advanced techniques beyond the scope of typical calculus courses.
The first term might be simplified using substitution, but the second term is likely non-elementary.
A numerical method is the only approach for solving it.
I can solve the integral using u-substitution.
I can solve the integral by parts.