Bài tập 53 trang 177 SGK Toán 12 NC

A. \({e^3} - \dfrac{7}{2}{e^2} + \ln \left( {1 + e} \right)\).  

B. \({e^2} - 7e + \dfrac{1}{{e + 1}}\).

C. \({e^3} - \dfrac{7}{2}{e^2} - \dfrac{1}{{{{\left( {e + 1} \right)}^2}}}\). 

D. \({e^3} - 7{e^2} - \ln \left( {1 + e} \right)\).

A. \(\dfrac{1}{{x{{\ln }^3}x}}\).                  

B. \(x{\ln ^3}x\).

C. \(\dfrac{{{x^2}}}{{{{\ln }^3}x}}\).                      

D. \(\dfrac{{{{\ln }^3}x}}{x}\).

A. \(\dfrac{6}{7}\)    

B. \(\dfrac{7}{6}\)  

C. 1      

D. 2   

A. \({\left( {a - x} \right)^{\dfrac{5}{2}}} + ax + C\). 

B. \( - \dfrac{2}{5}{\left( {a - x} \right)^{\dfrac{5}{2}}} + ax + C\).

C.\({\left( {a - x} \right)^{\dfrac{5}{2}}} - a + C\).      

D. \(\dfrac{2}{5}{\left( {a - x} \right)^{\dfrac{5}{2}}} - \dfrac{2}{3}a{\left( {a - x} \right)^{\dfrac{3}{2}}} + C\).

A. \({V_y} = 12\pi \).         

B. \({V_y} = 8\pi \). 

C. \({V_y} = 18\pi \).     

D. \({V_y} = 16\pi \). 

A. \( - \dfrac{1}{x} - \dfrac{2}{{{x^2}}} - \dfrac{4}{{3{x^2}}} + C\).

B. \(\dfrac{1}{x} - \dfrac{2}{{{x^2}}} - \dfrac{4}{{3{x^2}}} + C\).

C. \( - \dfrac{1}{x} - \dfrac{1}{{{x^2}}} - \dfrac{1}{{{x^3}}} + C\).    

D. \( - \dfrac{1}{x} + \dfrac{2}{{{x^2}}} - \dfrac{4}{{3{x^2}}} + C\).

A. 32                              

B. 34   

C. 46                              

D. 40