List of top Mathematics Questions on Integral Calculus asked in AP EAMCET

If \[ \int \log \left( 6\sin^2x + 17\sin x + 12 \right)^{\cos x} \, dx = f(x) + c \] then, \[ f\left(\frac{\pi}{2}\right) = \]

Evaluate the integral: \[ \int \left[ (\log_2 x)^2 + 2 \log_2 x \right] dx. \]

Given that: $M = \int_{0}^{\infty} \frac{\log t}{1 + t^3} \, dt$, and $N = \int_{-\infty}^{\infty} \frac{e^{2t} t}{1 + e^{3t}} \, dt$. Then, the relation between $M$ and $N$ is: