Questions in indefinite-integration

Select	Question
	$\int_{{}}^{{}}{\sqrt{1+\sin \frac{x}{2}}\ dx=}$
	$\int_{{}}^{{}}{({{\sin }^{-1}}x+{{\cos }^{-1}}x)\ dx=}$
	$\int_{{}}^{{}}{\frac{\sin x+\cos x}{\sqrt{1+\sin 2x}}\ dx=}$
	$\int_{{}}^{{}}{\frac{x-1}{{{(x+1)}^{2}}}\ dx=}$
	$\int_{{}}^{{}}{\frac{\text{cosec}\theta -\cot \theta }{\text{cosec}\theta +\cot \theta }}\ d\theta =$
	$\int_{{}}^{{}}{(1+2x+3{{x}^{2}}+4{{x}^{3}}+......)\ dx=}$
	If $\int_{{}}^{{}}{(\cos x-\sin x)\ dx=\sqrt{2}\sin (x+\alpha )+c}$, then $\alpha =$
	$\int_{{}}^{{}}{\frac{3{{x}^{2}}-2\sqrt{x}}{x}}dx=$
	If $\int_{{}}^{{}}{\frac{dx}{1+\sin x}=\tan \left( \frac{x}{2}+a \right)+b}$, then
	$\int_{{}}^{{}}{\frac{dx}{\sin x+\cos x}}=$