Indefinite Integration JEE Main PYQs, 2020 to 2025

Let ${\mathrm{I}}(x)=\int \frac{dx}{(x-11)^{{\frac{11}{13}}}(x+15)^{{\frac{15}{13}}}}$. If ${\mathrm{I}}(37)-{\mathrm{I}}(24)=\frac{1}{4}\left(\frac{1}{{\ \mathrm{b}}^{{\frac{1}{13}}}}-\frac{1}{{\mathrm{c}}^{{\frac{1}{13}}}}\right),{\mathrm{b}},{\mathrm{c}}\in {\mathcal{N}}$, then $3({\ \mathrm{b}}+{\mathrm{c}})$ is equal to

Let $\int x^{3}\sin x{\ \mathrm{d}}x=g(x)+C$, where $C$ is the constant of integration. If $8\left(g\left(\frac{\pi}{2}\right)+g^{{'}}\left(\frac{\pi}{2}\right)\right)=\alpha\pi^{3}+\beta\pi^{2}+\gamma,\alpha,\beta,\gamma\in Z$, then $\alpha+\beta-\gamma$ equals :