List of top Mathematics Questions on Integrals of Some Particular Functions

\( \int \frac{dx}{\sqrt{e^{-2x} - 1}} \) is equal to :
\(\int \frac{1}{\sqrt{2x-x^2}}dx =\)
If \(a > 0,b > 0\) and \(\int \frac{1}{ax^2+b}dx = \frac{1}{\sqrt{6}}tan^{-1}(\frac{\sqrt{2}x}{\sqrt{3}})+c\), then \(\int \frac{1}{bx^2+a}dx = \ldots\)
\(\int cot^4x\,dx\) is equal to
\(\int e^{2x}\frac{2(sin2xcos2x-1)}{2sin^22x}\,dx = A\,e^{2x}cot2x+c\)
(Where c is the constant of integration.), then \(A^3 =\)
The value of \(\int \frac{1}{x^2-5x+8}dx\) is equal to...
If \(\int \frac{dx}{\sqrt{2ax-x^2}} = f(g(x))+c\), where \(c\) is constant of integration, then \(f(x),g(x)\) are respectively equal to
$\int (\cot 2x + \csc 2x) dx = $

\(\int \frac{10e^x}{(2e^x + 5)^3} dx\) is equal to 
 

Evaluate \[ \int\frac{\cos x}{\sqrt{16\cos^2x+9}}dx \]
The integral of the function \( \frac{1}{9 - 4x^2} \) is :
$\int(\sin^{-1}\sqrt{x}+\cos^{-1}\sqrt{x})dx=$ ________.
$\int\frac{\sin 2x}{\sin x}dx=$ ________.
\( \int \frac{1}{\sqrt{9+8x-x^2}}\,dx = \varphi(x) + c \), then \( \varphi(x) = \)
Evaluate the integral: \( \int \sin^5 x \, dx \)
If $\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\right|+$ constant, then $\beta-\alpha$ is equal to_______
Let $f(x)=\int \frac{2 x}{\left(x^2+1\right)\left(x^2+3\right)} d x$ If $f(3)=\frac{1}{2}\left(\log _e 5-\log _e 6\right)$, then $f(4)$ is equal to
The value of $\displaystyle\lim _{n \rightarrow \infty} \frac{1+2-3+4+5-6+\ldots +(3 n-2)+(3 n-1)-3 n}{\sqrt{2 n^4+4 n+3-} \sqrt{n^4+5 n+4}}$ is :
If $\int \limits_0^\pi \frac{5^{\cos x}\left(1+\cos x \cos 3 x+\cos ^2 x+\cos ^3 x \cos 3 x\right) d x}{1+5^{\cos x}}=\frac{ k \pi}{16}$, then $k$ is equal to
The integral \(16 \int\limits_1^2 \frac{d x}{x^3\left(x^2+2\right)^2}\)  is equal to

Let S be the set of all integral values of \( \alpha \) for which the sum of squares of two real roots of the quadratic equation \( 3{x^2} + (\alpha - 6)x + (\alpha + 3) = 0 \) is minimum. Then S :

If \[ \int \frac{dx}{x^{2022}(1+x^{2022})^{\frac{1}{2022}}} = -\frac{(1+x^m)^{\frac{n}{m}}}{nx^n}+C, \] then \(m-n=\)
Evaluate the integral: $\int \frac{10^{x/2}}{\sqrt{10^{-x} - 10^x}} dx$
If $f\left(x\right) = \frac{2- x\cos x}{2+x \cos x}$ and $ g\left(x\right) =\log_{e}x ., \left(x>0\right) $ then the value of integral $\int\limits^{\frac{\pi}{4}}_{-\frac{\pi}{4}} g\left(f\left(x\right)\right)dx $ is :
If $\int \frac{dx}{x^{3}\left(1+x^{6}\right)^{\frac{2}{3}}}=f \left(x\right)\left(1+x ^{6}\right)^{\frac{1}{3}}+C$, where C is a constant of integration, then the function $f \left(x\right)$ is equal to-