Integrals Test ...

$$\int ^{\pi /2}_{-\pi /2} cost . \sin(2t-\displaystyle \frac{\pi}{4})dt=$$

$$\displaystyle \int_{0}^{a}\frac{dx}{x+\sqrt{a^{2}-x^{2}}}=$$

$$\displaystyle \int_{0}^{\pi/2}\sqrt{\cos x}\sin^{5}xdx=$$

$$\displaystyle \int_{0}^{\pi/2}\frac{1}{a+bcosx}dx=$$, where $$a>|b|$$

$$\displaystyle \int_{1}^{2}\mathrm{x}^{2\mathrm{x}}[1+\log \mathrm{x}]\mathrm{d}\mathrm{x}=$$

lf $$\displaystyle \int_{0}^{\infty}e^{-\mathrm{x}^{2}}\mathrm{d}\mathrm{x}=\frac{\sqrt{\pi}}{2}$$, then $$\displaystyle \int_{0}^{\infty}e^{-ax^{2}}dx,\ \mathrm{a}>0$$ is

Observe the following Lists

If $$\displaystyle \int_{0}^{\pi/3}\frac{\cos x}{3+4\sin x}dx=k\log(\frac{3+2\sqrt{3}}{3})$$, then $$\mathrm{k}$$ is equal to

The value of the integral 
$$\displaystyle \int_{0}^{3\alpha}\text{cosec}(x -\alpha)\text{cosec}(x-2\alpha) dx$$ is

If $$I_{n}=\displaystyle \int_{0}^{\frac{\pi}{4}}\tan^{n} dx,$$ then $$\dfrac{1}{I_{2}+I_{4}},\dfrac{1}{I_{3}+I_{5}},\dfrac{1}{I_{4}+I_{6}}\cdots$$ form