3.$\int_{0}^{+\infty }{\frac{\ln x}{{{(1+x)}^{2}}}}dx=$( )
A. $0$
B. $1$
C. $2$
D. $4$
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2.$\int_{-\infty }^{+\infty }{\frac{dx}{{{x}^{2}}+4x+9}}=$( )
A. $\frac{\pi }{3}$
B. $\frac{\pi }{2}$
C. $\frac{\pi }{\sqrt{13}}$
D. $\frac{\pi }{\sqrt{5}}$
1.$\int_{0}^{+\infty }{\frac{1}{{{(1+{{e}^{x}})}^{2}}}dx}=$( )
A. $\ln 2+\frac{1}{2}$
B. $\ln 2-\frac{1}{2}$
C. $\ln 2+\frac{1}{4}$
D. $\ln 2-\frac{1}{4}$
9.$\int_{{}}^{{}}{\frac{xdx}{(1+{{x}^{2}})\sqrt{1-{{x}^{2}}}}}=$()。
A. $-\frac{1}{2\sqrt{2}}\ln \left| \frac{\sqrt{2}+\sqrt{1-{{x}^{2}}}}{\sqrt{2}-\sqrt{1-{{x}^{2}}}} \right|+C$
B. $-\frac{1}{2\sqrt{2}}\ln \left| \frac{\sqrt{2}+(1+{{x}^{2}})}{\sqrt{2}-\sqrt{1-{{x}^{2}}}} \right|+C$
C. $-\frac{1}{2\sqrt{2}}\ln \left| \frac{\sqrt{2}-(1+{{x}^{2}})}{\sqrt{2}-\sqrt{1-{{x}^{2}}}} \right|+C$
D. $-\frac{1}{2\sqrt{2}}\ln \left| \frac{\sqrt{2}+\sqrt{1+{{x}^{2}}}}{\sqrt{2}-\sqrt{1+{{x}^{2}}}} \right|+C$
8.$\int_{{}}^{{}}{\frac{dx}{{{x}^{2}}+2x+5}}=$()。
A. $\arctan \frac{x-1}{2}+C$
B. $\arctan \frac{x+1}{2}+C$
C. $\frac{1}{2}\arctan \frac{x-1}{2}+C$
D. $\frac{1}{2}\arctan \frac{x+1}{2}+C$
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