Nguyên hàm !!

A.\[F'\left( x \right) = f''\left( x \right)\]

B. \[F'\left( x \right) = f'\left( x \right)\]

C. \[F'\left( x \right) = f'\left( x \right)\]

D. \[f'\left( x \right) = F\left( x \right)\]

A.\[f'\left( x \right) = F\left( x \right)\]

B. \[\smallint f\left( x \right)dx = F\left( x \right) + C\]

C. \[\smallint F\left( x \right)dx = f\left( x \right) + C\]

D. \[f'\left( x \right) = F'\left( x \right)\]

A.\[\smallint f'\left( x \right)dx = f\left( x \right) + C\]

B. \[\smallint f\left( x \right)dx = f'\left( x \right) + C\]

C. \[\smallint f'\left( x \right)dx = f''\left( x \right) + C\]

D. \[\smallint f\left( x \right)dx = f''\left( x \right) + C\]

A.\[y = 12{x^3}\]

B. \[y = \frac{{3{x^5}}}{5} - 1\]

C. \[y = \frac{{3{x^5} + 1}}{5}\]

D. \[y = \frac{3}{5}{x^5} - \frac{3}{5}\]

A.\[\smallint \left[ {f\left( x \right) + g\left( x \right)} \right]dx = \smallint f\left( x \right)dx + \smallint g\left( x \right)dx\] với mọi hàm\[f\left( x \right);g\left( x \right)\]liên tục trên R.

B. \[\smallint \left[ {f\left( x \right) - g\left( x \right)} \right]dx = \smallint f\left( x \right)dx - \smallint g\left( x \right)dx\] với mọi hàm\[f\left( x \right);g\left( x \right)\]liên tục trên R.

C. \[\smallint \left[ {kf\left( x \right)} \right]dx = k\smallint f\left( x \right)dx\] với mọi hằng số k và hàm f(x) liên tục trên R.

D. \[\smallint \left[ {f'\left( x \right)} \right]dx = f(x) + C\]  với mọi f(x) có đạo hàm trên R.

A.\[y = \sin x + 1\]

B. \[y = \cos x\]

C. \[y = \cot x\]

D. \[y = - \cos x\]Trả lời:

A.\[\smallint \sin xdx = \cos x + C\]

b. \[\smallint dx = x + C\]

C. \[\smallint {e^x}dx = {e^x} + C\]

D. \[\smallint \frac{1}{x}dx = \ln \left| x \right| + C\]

A.\[\smallint 0dx = C\]

B. \[\smallint dx = C\]

C. \[\smallint dx = 0\]

D. \[\smallint 0dx = x + C\]

A.\[\smallint {a^x}dx = \frac{{{a^x}}}{{\ln a}} + C(0 < a \ne 1)\]

B. \[\smallint {a^x}dx = {a^x} + C(0 < a \ne 1)\]

C. \[\smallint {a^x}dx = {a^x}\ln a + C(0 < a \ne 1)\]

D. \[\smallint {a^x}dx = {a^x}\ln a(0 < a \ne 1)\]

A.\[\smallint 0dx = C\]

B. \[\smallint dx = C\]

C. \[\smallint dx = 0\]

D. \[\smallint 0dx = x + C\]

A. \[\smallint \frac{1}{{x + 2}}dx = \ln \left( {x + 2} \right) + C\]

B.\[y = \ln \left( {3\left| {x + 2} \right|} \right)\] là một nguyên hàm của f(x)

C.\[y = \ln \left| {x + 2} \right| + C\] là họ nguyên hàm của f(x)

D.\[y = \ln \left| {x + 2} \right|\] là một nguyên hàm của f(x)

A.\[{x^2}\left( {1 + \frac{3}{4}{x^2}} \right) + C\]

b. \[\frac{{{x^2}}}{2}\left( {2x + {x^3}} \right) + C\]

C. \[{x^2}\left( {2 + 6x} \right) + C\]

D. \[{x^2} + \frac{3}{4}{x^4}\]

A.\[\smallint f(x)dx = \frac{{{x^3}}}{3} - \frac{2}{x} + C.\]

B. \[\smallint f(x)dx = \frac{{{x^3}}}{3} - \frac{1}{x} + C.\]

C. \[\smallint f(x)dx = \frac{{{x^3}}}{3} + \frac{2}{x} + C.\]

D. \[\smallint f(x)dx = \frac{{{x^3}}}{3} + \frac{1}{x} + C.\]

A.\[F\left( x \right) = - \frac{1}{{2018}}{e^{ - 2018x + 2017}} + \frac{1}{{2018e}}\]

B. \[F\left( x \right) = - \frac{1}{{2018}}{e^{ - 2018x + 2017}} + e + \frac{1}{{2018e}}\]

C. \[F\left( x \right) = - 2018{e^{ - 2018x + 2017}} + e + \frac{{2018}}{e}\]

D. \[F\left( x \right) = - 2018{e^{ - 2018x + 2017}} + \frac{1}{{2018e}}\]

A.\[ - 4{x^2} + 3x + C.\]

B. \[ - 4{x^2} + 2x + C.\]

C. \[4{x^2} + 2x + C.\]

D. \[ - 4{x^2} + x + C.\]

A.P=−4

B.P=1

C.P=−5

D.P=−3

A.3      

B.4  

C.8    

D.-1

A.\[\frac{2}{3}\ln \left| {2x + 1} \right| + \frac{5}{3}\ln \left| {x - 1} \right| + C\]

B. \[ - \frac{2}{3}\ln \left| {2x + 1} \right| + \frac{5}{3}\ln \left| {x - 1} \right| + C\]

C. \[\frac{2}{3}\ln \left| {2x + 1} \right| - \frac{5}{3}\ln \left| {x - 1} \right| + C\]

D. \[ - \frac{1}{3}\ln \left| {2x + 1} \right| + \frac{5}{3}\ln \left| {x - 1} \right| + C\]Trả lời:

A.\[\frac{{{x^2} + x - 1}}{{x + 1}}\]

B. \[\frac{{{x^2} - x - 1}}{{x + 1}}\]

C. \[\frac{{{x^2} + x + 1}}{{x + 1}}\]

D. \[\frac{{{x^2}}}{{x + 1}}\]

A.264334 con

B.256334 con

C.300560 con

D.614678 con

A.\[\sqrt {15} \]

B. \[\sqrt {23} \]

C. \[\sqrt {24} \]

D. \[\sqrt {26} \]

A.\[\smallint f\left( x \right)dx = 2x + C\]

B. \[\smallint f\left( x \right)dx = {x^2} + 4x + C\]

C. \[\smallint f\left( x \right)dx = \frac{{{x^3}}}{3} + 4x + C\]

D. \[\smallint f\left( x \right)dx = {x^3} + 4x + C\]

A.\[\smallint f\left( x \right)dx = {e^{x - 2}} + C\]

B. \[\smallint f\left( x \right)dx = {e^x} + 2x + C\]

C. \[\smallint f\left( x \right)dx = {e^x} + C\]

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

A.\[x + \frac{1}{{x - 2}} + C\]

B. \[\frac{{{x^2}}}{2} + \ln \left| {x - 2} \right| + C\]

C. \[{x^2} + \ln \left| {x - 2} \right| + C\]

D. \[1 + \frac{1}{{{{\left( {x - 2} \right)}^2}}} + C\]

A.340 (mét)

B.420 (mét)

C.400 (mét)

D.320 (mét)