Tìm số dương a sao cho \(\int\limits_0^a {\frac{{{x^2} + 2x + 2}}{{x + 1}}} {\rm{d}}x = \frac{{{a^2}}}{2} + a + \ln 3.\)

Tìm số dương a sao cho \(\int\limits_0^a {\frac{{{x^2} + 2x + 2}}{{x + 1}}} {\rm{d}}x = \frac{{{a^2}}}{2} + a + \ln 3.\)
A. a=5
B. a=4
C. a=3
D. a=2

Ta có:
\( \int_0^a {\frac{{{x^2} + 2x + 2}}{{x + 1}}dx} = \int_0^a {[(x + 1) + \frac{1}{{x + 1}}]dx = \left. {\left( {\frac{{{x^2}}}{2} + x + \ln |x + 1|} \right)} \right|_0^a = \frac{{{a^2}}}{2} + a + \ln (a + 1)} .\)
Suy ra a=2.