Question

If $\int\limits_0^1\left(x^{21}+x^{14}+x^7\right)\left(2 x^{14}+3 x^7+6\right)^{1 / 7} d x=\frac{1}{l}(11)^{m / n}$ where $l, m, n \in N , m$ and $n$ are coprime then $l+m+n$ is equal to ______

Answer 1

The correct answer is 63.
∫(x20+x13+x6)(2x21+3x14+6x7)1/7dx
2x21+3x14+6x7=t
42(x20+x13+x6)dx=dt
421​0∫11​t71​dt=(78​t78​​×421​)011​
=481​(t78​)011​=481​(11)8/7
l=48,m=8,n=7
l+m+n=63