Bài tập Nguyên hàm của hàm số mũ lớp 12 (có lời giải)

A. 3e^x + C;

B. \(\frac{1}{3}{e^{3x}} + C\);

C. \(\frac{1}{3}{e^x} = C\);

D. 3e^3x + C.

A. \(\int {f\left( x \right)dx} = {e^{x - 2}} + C\);

B. \(\int {f\left( x \right)dx} = {e^x} + 2x + C\);

C. \(\int {f\left( x \right)dx} = {e^x} + C\);

D. \(\int {f\left( x \right)dx} = {e^x} - 2x + C\).

A. \(\int {{2^x}dx} = \ln {2.2^x} + C\);

B. \(\int {{2^x}dx} = {2^x} + C\);

C. \(\int {{2^x}dx} = \frac{{{2^x}}}{{\ln 2}} + C\);

D. \(\int {{2^x}dx} = \frac{{{2^x}}}{{x + 1}} + C\).

A. \(\int {\left( {{3^x} + 2x} \right)dx} = \frac{{{3^x}}}{{\ln 3}} + {x^2} + C\);

B. \(\int {\left( {{3^x} + 2x} \right)dx} = {3^x}.\ln 3 + {x^2} + C\);

C. \(\int {\left( {{3^x} + 2x} \right)dx} = \frac{{{3^x}}}{{\ln 3}} + x + C\);

D. \(\int {\left( {{3^x} + 2x} \right)dx} = {3^x}.\ln 3 + x + C\).

A. \(\int {f\left( x \right)dx} = \frac{{2{e^{3x}}}}{3} - 3{e^x} + C\);

B. \(\int {f\left( x \right)dx} = \frac{{2{e^{3x}}}}{3} + 3{e^x} + C\);

C. \(\int {f\left( x \right)dx} = {e^x}\left( {{e^{2x}} - 3} \right) + C\);

D. \(\int {f\left( x \right)dx} = \frac{{{e^{3x}}}}{3} + 3{e^x} + C\).

A. \(\int {f\left( x \right)dx} = \frac{{{4^x}}}{{\ln 4}} - \frac{{\sin 2x}}{2} + C\);

B. \(\int {f\left( x \right)dx} = {4^x}\ln 4 + \frac{{\sin 2x}}{2} + C\);

C. \(\int {f\left( x \right)dx} = {4^x}\ln 4 - \frac{{\sin 2x}}{2} + C\);

D. \(\int {f\left( x \right)dx} = \frac{{{4^x}}}{{\ln 4}} + \frac{{\sin 2x}}{2} + C\).

A. \(F\left( x \right) = - \frac{2}{{{e^x}}} + \tan x + C\);

B. \(F\left( x \right) = 2{e^x} - \tan x + C\);

C. \(F\left( x \right) = - \frac{2}{{{e^x}}} - \tan x + C\);

D. \(F\left( x \right) = 2{e^{ - x}} + \tan x + C\).

A. \(\frac{{{x^3}}}{3} - \frac{{{3^x}}}{{\ln 3}} - \frac{1}{{{x^2}}} + C\);

B. \(\frac{{{x^3}}}{3} - {3^x} + \frac{1}{{{x^2}}} + C\);

C. \(\frac{{{x^3}}}{3} - \frac{{{3^x}}}{{\ln 3}} + \ln \left| x \right| + C\);

D. \(\frac{{{x^3}}}{3} - \frac{{{3^x}}}{{\ln 3}} - \ln \left| x \right| + C\).

A. \({e^x} - 2{e^{ - 2x}} + C\);

B. \({e^x} + 2{e^{ - 2x}} + C\);

C. \({e^x} - \frac{1}{2}{e^{ - 2x}} + C\);

D. \(\frac{{{e^{x + 1}}}}{{x + 1}} + \frac{{{e^{ - 2x + 1}}}}{{ - 2x + 1}} + C\).

A. \({x^2} + \frac{{{e^{2020x}}}}{{2020}} + C\);

B. \({x^3} + \frac{{{e^{2020x}}}}{{2020}} + C\);

C. \(\frac{{{x^2}}}{2} + \frac{{{e^{2020x}}}}{{2020}} + C\);

D. \(x + \frac{{{e^{2020x}}}}{{2020}} + C\).