$\int_{0}^{2}{\frac{dx}{\sqrt{\left| 1-x \right|}}}=$( )
A. $0$
B. $2$
C. $4$
D. $6$
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$\int_{0}^{1}{\sqrt{\frac{x}{1-x}}dx}=$( )
A. $\frac{\pi }{2}$
B. $\frac{\pi }{4}$
C. $\frac{\pi }{6}$
D. $\frac{\pi }{8}$
$\int_{0}^{+\infty }{\frac{dx}{(x+1)\sqrt{{{x}^{2}}+1}}}=$( )
A. $\frac{1}{2}\ln (3+2\sqrt{2})$
B. $\frac{1}{2}\ln (3-2\sqrt{2})$
C. $\frac{\sqrt{2}}{2}\ln (3+2\sqrt{2})$
D. $\frac{\sqrt{2}}{2}\ln (3-2\sqrt{2})$
$\int_{{}}^{{}}{\frac{\sin x}{1+\sin x}dx}=$()。
A. $\frac{1}{\cos x}+\tan x+x+C$
B. $\frac{1}{\cos x}-\tan x-x+C$
C. $\frac{1}{\cos x}-\tan x+x+C$
D. $\frac{1}{\cos x}+\tan x-x+C$
$\int_{{}}^{{}}{\frac{{{x}^{2}}}{{{x}^{2}}+1}\arctan xdx}=$()。
A. $x\arctan x-\frac{1}{2}\ln (1+{{x}^{2}})-\frac{1}{2}{{(\arctan x)}^{2}}+C$
B. $x\arctan x+\frac{1}{2}\ln (1+{{x}^{2}})-\frac{1}{2}{{(\arctan x)}^{2}}+C$
C. $x\arctan x-\frac{1}{2}\ln (1+{{x}^{2}})+\frac{1}{2}{{(\arctan x)}^{2}}+C$
D. $x\arctan x+\frac{1}{2}\ln (1+{{x}^{2}})+\frac{1}{2}{{(\arctan x)}^{2}}+C$
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