Mathematics - Definite Integration Question with Solution | TestHub

Let

$I=\int \left(x^{20}+x^{13}+x^6\right){\left(2x^{21}+3x^{14}+6x^7\right)}^{\frac{1}{7}}dx$

Put

$2x^{21}+3x^{14}+6x^7=t$

$\Rightarrow 42\left(x^{20}+x^{13}+x^6\right)dx=dt$

$\therefore I=\frac{1}{42}{\int }_0^{11}{t}^{\frac{1}{7}}dt$

$\Rightarrow I=\frac{1}{42}{\left[\frac{7t^{\frac{8}{7}}}{8}\right]}_0^{11}$

$\Rightarrow I=\frac{1}{48}{\left(11\right)}^{\frac{8}{7}}$

So,

$l=48, m=8,n=7$

$\therefore l+m+n=63$