Cho \(I = 56\int_0^a {\frac{x}{{1 + {x^2}}}dx} ,\l...

B

- Hướng dẫn giải

\(I = 56\int_0^a {\frac{x}{{1 + {x^2}}}dx} ,\left( {a \in R} \right)\)

Đặt 

\(\begin{array}{l}
u = 1 + {x^2} \Rightarrow du = 2xdx \Rightarrow xdx = \frac{1}{2}du\\
x = 0 \Rightarrow u = 1,x = a \Rightarrow u = 1 + {a^2}
\end{array}\)

Vậy \(I = 28\int_1^{1 + {a^2}} {\frac{1}{u}du = 28\ln u\left| {_1^{1 + {a^2}}} \right. = 28\ln \left( {1 + {a^2}} \right)} \)