Tìm nguyên hàm
$\int{{\frac{{\sin x-\cos x}}{{\sin x+c\text{os}x}}dx}}.$
A. $\ln \left| {\sin x-c\text{os}x} \right|+C.$   
B. $-\ln \left| {\sin x-c\text{os}x} \right|+C.$   
C. $\ln \left| {\sin x+c\text{os}x} \right|+C.$  
D. $-\ln \left| {\sin x+c\text{os}x} \right|+C.$

Tìm nguyên hàm
$\int{{\frac{{\cos 2x}}{{{{{\sin }}^{2}}x{{{\cos }}^{2}}x}}dx}}.$
A. $\displaystyle \frac{{-2}}{{\sin 2x}}+C.$
B. $\displaystyle \frac{{-4}}{{\sin 2x}}.$
C. $\displaystyle \frac{2}{{\sin 2x}}+C.$
D. $\displaystyle \tan x+\cot x+C.$

Cho F(x) là một nguyên hàm của hàm số f(x)=1xlnx$\displaystyle $ và F(e) = 3. Tính F(1e).
A.
B.
C.
D.

Nguyên hàm $I=\int{{\frac{{\sin 2xdx}}{{3+4\sin x-\cos 2x}}}}$ bằng?
A.  $\displaystyle \frac{1}{2}\ln |{{\sin }^{2}}x+2\sin x+1|-\frac{1}{{\sin x+1}}+C$
B. $\displaystyle \frac{1}{2}\ln |{{\sin }^{2}}x+2\sin x+1|+\frac{1}{{\sin x+1}}+C$
C. $\displaystyle -\frac{1}{2}\ln |{{\sin }^{2}}x+2\sin x+1|-\frac{1}{{\sin x+1}}+C$
D. $\displaystyle -\frac{1}{2}\ln |{{\sin }^{2}}x+2\sin x+1|+\frac{1}{{\sin x+1}}+C$

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

Tìm nguyên hàm
$\int{{\frac{1}{{{{e}^{{4x}}}}}}}dx.$
A. $A.$ $\frac{1}{{-4}}{{e}^{{-4x}}}+C.$                
B. $B.$ $\frac{1}{4}{{e}^{{-4x}}}+C.$  
C. $C.$ ${{e}^{{-4x}}}+C.$    
D.    $D.$ $\frac{4}{{{{e}^{{4x}}}}}+C.$

Tìm nguyên hàm của hàm số f(x) = 22x.3x.7x.
A. $\frac{{{{{84}}^{x}}}}{{\ln 84}}+C.$
B. $\displaystyle {{84}^{x}}+C.$
C. $\frac{{{{2}^{{2x}}}{{{.3}}^{x}}{{{.7}}^{x}}}}{{\ln 2.\ln 3.\ln 7}}+C.$
D. $\frac{{{{2}^{{2x}}}{{{.3}}^{x}}{{{.7}}^{x}}}}{{\ln 4.\ln 3.\ln 7}}+C.$

Nguyên hàm $\int{x{{e}^{-x}}dx}$ bằng
A. $-x{{e}^{-x}}+{{e}^{-x}}+C.$
B. $-x{{e}^{x}}-{{e}^{-x}}+C.$
C. $x{{e}^{-x}}+{{e}^{-x}}+C.$
D. $-x{{e}^{-x}}+C.$

Tìm nguyên hàm
$\int{{{{5}^{{2x}}}dx}}.$
A. $A.$$\displaystyle {{5}^{{2x}}}+C.$         
B. $B.$$\displaystyle \frac{1}{{10}}{{5}^{{2x}}}+C.$       
C. $C.$$\displaystyle \frac{1}{{\ln 5}}{{5}^{{2x}}}+C.$   
D. $D.$$\displaystyle \frac{1}{{2\ln 5}}{{5}^{{2x}}}+C.$

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