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List of top Mathematics Questions on Integration by Parts

\(∫xlog(1+x^2)dx=\)?
If $\int\limits_0^1\left(x^{21}+x^{14}+x^7\right)\left(2 x^{14}+3 x^7+6\right)^{1 / 7} d x=\frac{1}{l}(11)^{m / n}$ where $l, m, n \in N , m$ and $n$ are coprime then $l+m+n$ is equal to ______
If \(f(x) + f(\pi-x) = \pi^{2}\) then \(_{0}\int^{\pi}f(x) sinx dx\) ?
\(∫_0^1 (5xe^{2x}-tan(π/4)) dx=\)
If I=∫\(\frac{x^2dx}{(x\,sin\,x+cos\,x)^2}\)=f(x)+tan x+c, then f(x) is
the value of ∫\(\frac{dx}{x(1+log\,x)^3}\) is _______

the value of ∫cot2xdx is________________

Evaluate ∫cos2 xdx_________

\(\begin{array}{l} I_n\left(x\right)=\int_0^x\frac{1}{\left(t^2+5\right)^n}dt, n=1, 2, 3,\cdots\end{array}\)

Then

If \(\frac{d y}{d x}+2 y \tan x=\sin x, 0\)

\(\int \frac{e^{x^2}\left(2x+x^{3}\right)}{\left(3+x^{2}\right)^{2}} dx\)  is equal to :
$\quad\int_{0}^{1} \left[f \left(x\right)g'' \left(x\right)-f''\left(x\right)g \left(x\right)\right]$ dx is equal to : [Given f(0) = g(0) = 0]
If I(m,n) =$\int_0^1 t^m(1+t)n dt ,$ then the expression for I(m, n) in terms of I(m + 1, n - 1) is
The integral $ \int\limits^{1/2}_{-1/2} \bigg ([x] + \log \bigg ( \frac{1+ x}{1 - x} \bigg ) \bigg ) \, dx $ equals
The value of \(\int \frac{ln\,x}{(1+ln\,x)^2}dx\)=?
If I =$ \int sec ^4x \, cosec ^2x \,dx$ =K tan ^3x +L tan x+M cot x + const, then
If \(\int\frac{dx}{a^2\sin x+b^2\cos^2x}=\frac{1}{12}\tan^{-1}(3\tan x)+c,\)then the maximum value of a sinx + bcosx is____
Find \(\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{\sin^2x}{1+2^x} \;dx\)

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