List of top Mathematics Questions on Integration by Parts asked in MHT CET

Evaluate the integral: \[ \int \frac{4x^2 \cot^{-1}(x^3)}{1+x^6}\,dx \] (where \(C\) is a constant of integration)
$\int x^{2}\cos x~dx=$
$\int x^{2}\cos x~dx=$
The value of the integral \( \int_0^1 \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \, dx \) is:
The value of \( \sqrt{3} \csc 20^\circ - \sec 20^\circ \) is:
The value of the integral \( \int_0^2 |2x - 3| \, dx \) is:
Integrate the function \( \int e^x \left( \frac{1 + \sin x}{1 + \cos x} \right) dx \):
The integral \( \int \frac{\csc x}{\cos^2\left(1 + \log \tan \frac{x}{2}\right)} \, dx \) is equal to:
Evaluate the indefinite integral $\int \sec^{-1}x \, dx$
$\int e^{\tan x}(\sec ^2 x+\sec ^3 x \sin x) d x=$
Evaluate the integral: $$\int [\sin(\log x) + \cos(\log x)]\ dx$$