Questions in indefinite-integration

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$\int_{{}}^{{}}{\frac{dx}{\sqrt{1+x}+\sqrt{x}}=}$
$\int_{{}}^{{}}{\frac{\cos 2x-\cos 2\alpha }{\cos x-\cos \alpha }}dx=$
$\int_{{}}^{{}}{\frac{1-\tan x}{1+\tan x}\ dx=}$
$\int_{{}}^{{}}{{{a}^{x}}\ da=}$
The value of $\int_{{}}^{{}}{\cot x\ dx}$ is
The value of $\int_{{}}^{{}}{\frac{1}{{{x}^{4}}}\ dx}$ is
$\int_{{}}^{{}}{\frac{{{e}^{5\log x}}-{{e}^{4\log x}}}{{{e}^{3\log x}}-{{e}^{2\log x}}}\ dx=}$
$\int_{{}}^{{}}{\frac{{{x}^{4}}+{{x}^{2}}+1}{{{x}^{2}}-x+1}\ dx=}$
$\int_{{}}^{{}}{\sec x\ dx=}$
$\int_{{}}^{{}}{\sqrt{1+\sin x}\ dx=}$

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