Questions in definite-integral

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$\int_{0}^{1}{\sqrt{\frac{1-x}{1+x}}}\,dx$ equals
$\int_{1}^{e}{\frac{1}{x}\,dx}$ is equals to
$\int_{\,1}^{\,x}{\frac{\log {{x}^{2}}}{x}\,dx=}$
$\frac{1}{2}(e-3)$
$\int_{0}^{\pi /4}{{}}(\cos x-\sin x)dx+\int_{\pi /4}^{5\pi /4}{{}}(\sin x-\cos x)dx + \int_{2\pi }^{\pi /4}{{}}(\cos x-\sin x)\,dx$ is equal to
$\left( \int_{\,0}^{\,a}{x\,dx} \right)\le (a+4),$ then
The value of $\int_{\,-\,1}^{\,3}{\,{{\tan }^{-1}}\left( \frac{x}{{{x}^{2}}+1} \right)+{{\tan }^{-1}}\left( \frac{{{x}^{2}}+1}{x} \right)\,dx}$ is
$\int_{\,-\,1}^{\,0}{\frac{dx}{{{x}^{2}}+2x+2}=}$
The value of $\int_{\,0}^{\,1}{\frac{{{\tan }^{-1}}x}{1+{{x}^{2}}}dx}$ is
$\int_{1}^{\sqrt{3}}{\frac{1}{1+{{x}^{2}}}dx}$ is equal to

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