Integrals Test ...

$$\displaystyle \int_{0}^{1}\frac{d}{dx}$$ $$tan^{-1} \left( \displaystyle \frac { 1 }{ x }  \right) $$

Evaluate: $$\int _{ 0 }^{ \tfrac { \pi  }{ 4 }  }{ ({ \tan }^{ 4 }x+{ \tan }^{ 2 }x)dx }$$

Evaluate: $$\displaystyle \int_{1/2}^{1}\frac{1}{\sqrt{x-x^{2}}}dx$$

If $$f(x)=\begin{vmatrix}\sin x+\sin2x+\sin3x & \sin2x & \sin3x\\ 3+4\sin x & 3 & 4\sin x\\ 1+\sin x & \sin x & 1\end{vmatrix} $$, then the value of $$\displaystyle \int_{0}^{\frac{\pi}2}f(x)dx$$, is

Evaluate: $$\displaystyle \int_{0}^{\pi /4}\tan^{6}xdx$$

$$(\displaystyle \sum_{n=1}^{10}\int_{-2n-1}^{-2n}\sin^{27}xdx)+(\sum_{n=1}^{10}\int_{2n}^{2n+1}\mathrm{s}in^{27}$$ $$xdx)=$$

lf $$I_{\mathrm{n}}=\displaystyle \int_{0}^{\dfrac{\pi}{4}}$$ $$\tan^{n} xdx$$, then $$\displaystyle \lim_{n\rightarrow\infty}n[I_{n}+I_{n+2}]=$$

The value of $$\displaystyle \int_{3}^{5}\frac{x^{2}}{x^{2}-4} dx$$ is

Evaluate the integral
$$\displaystyle \int_{1}^{\sqrt[7]{2}}\frac{1}{x(2x^{7}+1)} dx$$

Evalaute: $$\displaystyle \int_{-\pi/2}^{\pi/2}\sqrt{\cos x-\cos^{3}x}\ dx$$