List of top Mathematics Questions on integral asked in KEAM

If $u = \int e^x \cos x \, dx,\; v = \int e^x \sin x \, dx$, then $u + v =$

\(\int \sin^3 x \, e^{\log \cos x} \, dx =\)

If \(\int \frac{2^{1/x}}{x^2} \, dx = k\,2^{1/x} + c\) then \(k\) is equal to

If $\int \left(3t^2\sin\left(\frac{1}{t}\right) - t\cos\left(\frac{1}{t}\right)\right) dt = f(t)\sin\left(\frac{1}{t}\right) + c$ then $f(2)$ is equal to

$\int e^x \left(\frac{1 - \sin x}{1 - \cos x}\right) dx =$

$\displaystyle \int \frac{\sin(\cot^{-1}x)}{1+x^2} \, dx$ is equal to:

$\displaystyle \int \left(\frac{1}{(1+x)^2} - \frac{2}{(1+x)^3}\right)e^x \, dx$ is equal to:

$\displaystyle \int \sqrt{1 + \sin\left(\frac{x}{8}\right)} \, dx =$

$\displaystyle \int \frac{x^4 - 1}{x + 1} \, dx$ is equal to:

$\displaystyle \int \frac{\sin t + \cos t}{13 + 36\sin^2 t} \, dt$ is equal to:

\( \int \left(\tan^{2}(2x) - \cot^{2}(2x)\right)\,dx \)

Evaluate the integral: \( \int \frac{1}{x^3} \sqrt{1 - \frac{1}{x^2}} \text{dx} = \)

The value of \(\int_{1}^{2} [x-1]\,dx\), where \([x]\) denotes the greatest integer function in \(x\), is equal to

\(\int \left(\frac{\sin 3x}{\sin x}-\frac{\cos 3x}{\cos x}\right)\,dx\) is equal to

$\int x(1-x)^{10}\,dx =$

\( \displaystyle \int \frac{dx}{\cos^{2/3}x\ \sin^{4/3}x} \) is

\( \displaystyle \int \ cot x (1-\ cosec x)e^x\,dx \) is

If $\frac{dy}{dx} = \frac{1}{8\left(\sqrt{16+\sqrt{25+\sqrt{x}}}\right)\left(\sqrt{25+\sqrt{x}}\right)\sqrt{x}}$, then $y =$

$\int e^{\left(x+\frac{1}{x}\right)}\left(\frac{x^{2}-1}{x^{2}}\right)dx =$

$\int e^{2\theta}(2\cos^{2}\theta-\sin 2\theta)\, d\theta =$

$\int \frac{9e^{x}+4e^{-x}}{9e^{x}-4e^{-x}}dx =$

$\int \frac{\sec x}{(\sec x+\tan x)^{9}}dx =$

If $\int \frac{1}{x^{7}\left(\frac{1}{x^{8}}+1\right)^{p}}dx = -\frac{1}{2}\left(\frac{1}{\frac{1}{x^{8}}+1}\right)^{2} + c$, then $p =$

\( \int e^x(x^2-2)\cos(e^x(x^2-2x)) dx = \)

\( \int e^x \sec x (1+\tan x) dx = \)