Cho hàm số $y = f(x)$ thỏa mãn $f'\left( x \right) = \left( {x + 1} \right){e^x}$ và $\int {f'(x)} dx = (ax + b){e^x} + c$ với $a, b, c$ là các hằng số. Chọn mệnh đề đúng:

$a \in \left( {\dfrac{1}{2};1} \right).$

$a \in \left( {1;\dfrac{3}{2}} \right).$

$a \in \left( {\dfrac{3}{2};2} \right).$

$a \in \left( {2;\dfrac{5}{2}} \right).$

\(y=\tan x\)                             

\(y=\cot x\)                             

\(y=\sin x\)                              

\(F'\left( x \right) = f''\left( x \right)\)

\(F'\left( x \right) = f'\left( x \right)\)             

\(F'\left( x \right) = f\left( x \right)\)

\(f'\left( x \right) = F\left( x \right)\)

$I = 12$

$I = 48$

$I = 8$

$I = 3$

\(I = \left. {\left( {\dfrac{{{u^3}}}{3} + u} \right)} \right|_1^2\)                  

\(I = \left. {\dfrac{4}{3}\left( {{u^3} + u} \right)} \right|_1^2\)

\(I = \left. {2\left( {\dfrac{{{u^3}}}{3} + u} \right)} \right|_1^2\)

\(I = \left. {\dfrac{1}{3}\left( {\dfrac{{{u^3}}}{3} + u} \right)} \right|_1^2\)

\(\int\limits_1^{{e^2}} {\ln xdx} \).

\(\int\limits_0^1 {2dx} \).

\(\int\limits_0^\pi  {\sin xdx} \).

\(\int\limits_0^2 {xdx} \).

\(\int\limits_a^b {f'\left( x \right){e^{f\left( x \right)}}dx}  = 0\)      

\(\int\limits_a^b {f'\left( x \right){e^{f\left( x \right)}}dx}  = 1\)

\(\int\limits_a^b {f'\left( x \right){e^{f\left( x \right)}}dx}  =  - 1\)  

\(\int\limits_a^b {f'\left( x \right){e^{f\left( x \right)}}dx}  = 2\)