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

\(\int \frac{logx}{(1+logx)^2}dx =\)
\(\int (e^{log(sinx)}+cosx)x\,dx =\)
The value of integral \(\int x^3cosx\,dx\) is...
The value of integral \(\int \frac{\sqrt{x^2+1}\,[log(x^2+1)-2logx]}{x^4}\,dx\) is equal to...
\(\int sin(logx)\,dx =\)
If \(f(x) = \frac{sin^{-1}x}{\sqrt{1-x^2}}\) and \(g(x) = e^{sin^{-1}x}\), then the value of \(\int f(x)g(x)\,dx = \ldots\)
\(\int x^3logx\,dx =\)
\(\int \text{cosec}^{-1}(\sqrt{\frac{a+x}{x}})\,\text{d}x =\)
If \(f(x)\) and \(g(x)\) are integrable functions then \([\int f(x)dx][\int g(x)dx] =\)
If an antiderivative of \(f(x)\) is \(e^x\) and an antiderivative of \(g(x)\) is \(cosx\), then \(\int f(x)cosx\,dx+\int g(x)e^x\,dx =\)
If \(\int x^2\cdot e^xdx = e^xf(x)+c\), then the minimum value of \(f(x)\) is ...
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: $$\int [\sin(\log x) + \cos(\log x)]\ dx$$