Questions in definite-integral

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The points of intersection of ${{F}_{1}}(x)=\int_{2}^{x}{(2t-5)\,dt}$ and ${{F}_{2}}(x)=\int_{0}^{x}{2t\,dt,}$ are
$\int_{0}^{\infty }{\frac{{{x}^{2}}\,dx}{({{x}^{2}}+{{a}^{2}})({{x}^{2}}+{{b}^{2}})}}=$
$\int_{0}^{\infty }{\frac{{{x}^{3}}\,dx}{{{({{x}^{2}}+4)}^{2}}}=}$
$\int_{0}^{\pi /2}{{{\sin }^{2m}}x\,dx=}$
$\int_{0}^{\pi /2}{{{\sin }^{5}}x\,dx=}$
$\int_{0}^{\infty }{\frac{x\,dx}{(1+x)(1+{{x}^{2}})}}=$
If $\varphi (x)=\int_{1/x}^{\sqrt{x}}{\sin ({{t}^{2}})\,dt,}$ then ${\varphi }'(1)=$
The value of integral $\int_{0}^{1}{\frac{{{x}^{b}}-1}{\log x}}\,dx$ is
The value of the integral $\int_{-1}^{1}{\frac{d}{dx}\left( {{\tan }^{-1}}\frac{1}{x} \right)}\,dx$ is
The least value of the function $F(x)=$ $\int_{5\pi /4}^{x}{(3\sin u+4\cos u)\,du}$ on the interval $\left[ \frac{5\pi }{4},\,\,\frac{4\pi }{3} \right]$ is

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