Questions in definite-integral

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If $(n-m)$ is odd and $|m|\,\ne \,|n|,$ then $\int_{0}^{\pi }{\cos mx\sin nx}\,dx$ is
To find the numerical value of $\int_{-2}^{2}{(p{{x}^{2}}+qx+s)\,dx,}$ it is necessary to know the values of constants
If $I=\int_{0}^{100\pi }{\sqrt{(1-\cos 2x)}\,dx,}$then the value of $I$ is
$\int_{-1}^{1}{\log \left( \frac{1+x}{1-x} \right)\,dx=}$
If $\int_{-1}^{4}{f(x)\,dx}=4$ and $\int_{2}^{4}{(3-f(x))\,dx=7,}$ then the value of $\int_{2}^{-1}{f(x)\,dx}$ is
The function $F(x)=\int_{0}^{x}{\log \left( \frac{1-x}{1+x} \right)}\,dx$ is
$\int_{-\pi /2}^{\pi /2}{\frac{\cos x}{1+{{e}^{x}}}\,dx=}$
The value of $\int_{-1}^{1}{(\sqrt{1+x+{{x}^{2}}}-\sqrt{1-x+{{x}^{2}}})\,dx}$ is
The value of $\int_{0}^{\pi /2}{\log \,\left( \frac{4+3\sin x}{4+3\cos x} \right)}\,dx$ is
The value of $\int_{0}^{1}{{{\tan }^{-1}}\left( \frac{2x-1}{1+x-{{x}^{2}}} \right)}\,dx$ is

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