List of top Mathematics Questions on Integrals of Some Particular Functions asked in AMUEEE

The value of the integral $ \int_{-2}^{0}\frac{dx}{\sqrt{12-x^{2}-4x}} $ is
The integral $ \int \sqrt{16-9x^2} $ $dx$ equals
The value of the integral $ \int_{0}^{1} $ $ \frac{e^{5log_{e}x}-e^{4log_{e}x}}{e^{log_{e}x^3}-e^{log_{e}x^2}}dx $ is
$ \int \frac{x^3dx}{1+x^4} $ equals
Given that $ \int_{0}^{\infty}\frac{x^{2}}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)\left(x^{2}+c^{2}\right)} $ dx = $ \frac{\pi}{2\left(a+b\right)\left(b+c\right)\left(c+a\right)'} $ then $ \int_{0}^{\infty}\frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)} $ is
If $ \int_{0}^{\frac{\pi}{3}}\frac{cos x}{3 + 4 sin x}dx = k\, log \left(\frac{3+2\sqrt{3}}{3}\right) $ then $k$ is
Let $ f $ be the function $ [-\pi, \pi] $ given by $ f(0) = 9 \,and\,f(x) \,=\, f(x) = sin (\frac {9x}{2})/sin(\frac {x}{2}) $ for $ x \neq 0 $ . The value of $ \frac{2}{\pi} \int^{\pi}_{-\pi} $ $ f(x) dx $ is
If $ I_{1}=\int_{0}^{\frac{\pi}{2}} f (sin \,2x)sin \,xdx $ and $ I_2 = \int^{\pi/4}_{0}\,f(cos2x) cosx \,dx\,then\, I_1/I_2 $ =
$ \int e^{xloga }e^{x} dx $ is equal to
$ \int e^{x}\left(cosec^{-1}x+\frac{-1}{x\sqrt{x^{2}-1}}\right) \, dx$ is equal to