List of top Mathematics Questions on integral asked in COMEDK UGET

The integral \( \int \frac{2^x}{\sqrt{1 - 4^x}} \, dx \) is equal to:
The integral \( \int_{\pi/2}^{-\pi/2} \sin x \, dx \) is:
If $\int\limits \frac{\cos \, 8x + 1}{ \tan \, 2x - \cot \, 2x} dx = a \, \cos \, 8x + c , $ then $a$ =
$\int\limits \frac{x^3 -1}{x^3 + x} dx = $
$ \int\limits_1^e \log \, x \, dx = $
The interval I such that $\int^1_0\frac{dx}{\sqrt{1+x^4}}\in \,I$ is given by
The value of $\int^2_{-2}(ax^3+bx +c)dx$ depends on the
$\int^{\frac{\pi}{2}}_0 \log(\tan\,x)dx=$
The solution of $\left(x+y\right)^{2} \left(x \frac{dy}{dx}+y\right)=xy \left(1 +\frac{dy}{dx}\right) $ is
$\int e^{x}\left(\cos x -\sin x\right)dx $ is equal to
If $\int f\left(x\right) dx =\Psi\left(x\right)$ then $ \int x^{5} f\left(x^{3}\right)dx $ is equal to
The intercepts on $x-axis$ made by tangents to the curve, $y = \displaystyle\int_0^x |t| dt, x \in R$, which are parallel to the line $y = 2x$, are equal to
If $ \int \frac{xe^{x}}{\left(1+x\right)^{2}} dx = e^{x} f\left(x\right) +c, $ then $f(x)$ is equal to
Let $f (x)$ and $g(x)$ be differentiable functions on (0, 2] such that $f"(x) - g"(x) = 0, f'(1) = 2g'(1) = 4, f(2) = 3g(2) = 9.$ Then $f (x)- g(x)$ at $ x = 3/2$ is
$ \int\limits_0^{\pi /8} \tan^2 (2x) dx = $
$\int\limits_{-1/2}^{1/2} \cos x\log\left(\frac{1+x}{1-x}\right) dx = $
$\int\limits_{1}^{e^{\frac{17}{2}}} \frac{\, \pi \cos (\pi \log x)}{x} dx =$
$\int \frac{x^{2}+1}{x^{4}+1}dx $
$\int e^{x} \left\{\frac{1+\sin x \cos x}{\cos^{2} x}\right\} dx = $
$\int \frac{2^{x+1} - 5^{x-1}}{10^{x}}dx = $
If $\int \frac{1}{x+x^{5}}dx =f\left(x\right)+c , $ then $\int \frac{x^{4}}{x+x^{5}} dx = $
If $[x]$ denotes the greatest integer function, then $\int\limits_{1}^{4} \left(\left[x\right] -1\right)\left(\left[x\right] -2\right)\left(\left[x\right] -3\right)\left(\left[x\right] -4\right)dx = $