List of top Mathematics Questions on Integral Calculus asked in MHT CET

Integrate the following function w.r.t. $x$: $\int \frac{e^{3x}}{e^{3x} + 1} \, dx$
If \( f(x) = 2x^3 - 15x^2 - 144x - 7 \), then \( f(x) \) is strictly decreasing in:
The general solution of
$$ \left(x\frac{dy}{dx} - y\right)\sin\frac{y}{x} = x^3 e^x $$ is: 
The surface area of a spherical balloon is increasing at the rate of \( 2 \, \text{cm}^2/\text{sec} \). Then the rate of increase in the volume of the balloon, when the radius of the balloon is \( 6 \, \text{cm} \), is:
If \( y = (\sin x)^y \), then \( \frac{dy}{dx} \) is: