Tìm nguyên hàm
$\int{{\frac{{{{e}^{{\frac{1}{x}}}}}}{{{{x}^{2}}}}dx}}.$
A. ${{e}^{{\frac{1}{x}}}}+C.$     
B. $-{{e}^{x}}+C.$
C. $-{{e}^{{\frac{1}{x}}}}+C.$   
D. $\frac{1}{{{{e}^{{\frac{1}{x}}}}}}+C.$

Tìm nguyên hàm
$\int{{\frac{{\sin x}}{{1-{{{\cos }}^{2}}x}}dx}}.$
A. $\displaystyle -\ln \left| {\frac{{\cos x-1}}{{\cos x+1}}} \right|+C.$
B. $\displaystyle \ln \left| {\frac{{\cos x-1}}{{\cos x+1}}} \right|+C.$
C. $\displaystyle -\frac{1}{2}\ln \left| {\frac{{\cos x-1}}{{\cos x+1}}} \right|+C.$
D. $\displaystyle \frac{1}{2}\ln \left| {\frac{{\cos x-1}}{{\cos x+1}}} \right|+C.$

Tìm nguyên hàm
$\int{{\frac{1}{{{{{(3-2x)}}^{5}}}}dx}}.$
A. $\displaystyle -\frac{1}{{4{{{(3-2x)}}^{4}}}}+C.$ 
B. $\displaystyle \frac{1}{{8{{{(3-2x)}}^{4}}}}+C.$
C. $\displaystyle -\frac{1}{{8{{{(3-2x)}}^{4}}}}+C.$
D. $\displaystyle \frac{1}{{4{{{(3-2x)}}^{4}}}}+C.$

Tìm m để nguyên hàm F(x) của f(x) thỏa mãn:
$f(x)=\frac{{4m}}{\pi }+{{\sin }^{2}}x;F(0)=1;F(\frac{\pi }{4})=\frac{\pi }{8}.$
A. $\displaystyle m=\frac{{-4}}{3}$
B. $\displaystyle m=-\frac{5}{3}$
C. $\displaystyle m=\frac{{-3}}{4}$
D. $\displaystyle m=\frac{3}{4}$

Tìm nguyên hàm
$\int{{\left( {x-1} \right){{e}^{{{{x}^{2}}-2x+3}}}dx}}.$
A. $\left( {\frac{{{{x}^{2}}}}{2}-x} \right){{e}^{{{{x}^{2}}-2x+3}}}+C.$   
B. $\left( {x-1} \right){{e}^{{\frac{1}{3}{{x}^{3}}-{{x}^{2}}+3x}}}+C.$
C. $\frac{1}{2}{{e}^{{{{x}^{2}}-2x}}}+C.$  
D. $\frac{1}{2}{{e}^{{{{x}^{2}}-2x+3}}}+C.$

Họ nguyên hàm của hàm số $f(x)={{x}^{2}}+{{x}^{3}}$ là
A. $\frac{{{{x}^{3}}}}{3}+\frac{{{{x}^{4}}}}{4}+C.$
B. $\frac{{{{x}^{3}}}}{3}-\frac{{{{x}^{4}}}}{4}+C.$
C. $2x+3{{x}^{2}}+C.$
D. $\frac{{{{x}^{3}}}}{2}+\frac{{{{x}^{4}}}}{3}+C.$

Nguyên hàm của hàm f(x) = cos(3 – 2x) là
A. $\frac{1}{3}\sin (-2x+3)+C.$
B. $\frac{1}{2}\sin (-2x+3)+C.$
C. $-\frac{1}{2}\sin (-2x+3)+C.$
D. $\frac{1}{{-3}}\sin (-2x+3)+C.$

 Nguyên hàm $I=\int{{\frac{{\tan x}}{{\cos x\sqrt{{1+{{{\cos }}^{2}}x}}}}dx}}$ bằng?
A. $\sqrt{{2+{{{\tan }}^{2}}x}}+C.$ 
B. $\frac{1}{2}\sqrt{{2+{{{\tan }}^{2}}x}}+C.$ 
C. $\sqrt{{2-{{{\tan }}^{2}}x}}+C.$ 
D. $\frac{1}{2}\sqrt{{2-{{{\tan }}^{2}}x}}+C.$

Tìm nguyên hàm $\int{{(\sqrt[3]{{{{x}^{2}}}}+\frac{4}{x})dx}}.$
A. $\frac{5}{3}\sqrt[3]{{{{x}^{5}}}}+4\ln \left| x \right|+C.$
B. $\frac{{-3}}{5}\sqrt[3]{{{{x}^{5}}}}+4\ln \left| x \right|+C.$
C. $\frac{3}{5}\sqrt[3]{{{{x}^{5}}}}-4\ln \left| x \right|+C.$
D. $\frac{3}{5}\sqrt[3]{{{{x}^{5}}}}+4\ln \left| x \right|+C.$

Tìm nguyên hàm $\int{{\frac{{x+3}}{{{{x}^{2}}+3x+2}}dx}}$.
A.  $\int{{\frac{{x+3}}{{{{x}^{2}}+3x+2}}dx}}=2\ln |x+2|-\ln |x+1|+C$.
B.  $\int{{\frac{{x+3}}{{{{x}^{2}}+3x+2}}dx}}=2\ln |x+1|-\ln |x+2|+C$.
C.  $\int{{\frac{{x+3}}{{{{x}^{2}}+3x+2}}dx}}=2\ln |x+1|+\ln |x+2|+C$.
D. $\int{{\frac{{x+3}}{{{{x}^{2}}+3x+2}}dx}}=\ln |x+1|+2\ln |x+2|+C$.