Hướng dẫn giải

Đặt \(\left\{ \begin{array}{l}u = x\\dv = {\tan ^2}xdx\end{array} \right. \Rightarrow \left\{ \begin{array}{l}du = dx\\v = \tan x - x\end{array} \right..\)

\(I = \left( {x\tan x - {x^2}} \right)\left| {_{\scriptstyle\atop\scriptstyle0}^{\scriptstyle1\atop\scriptstyle}} \right. - \int\limits_0^1 {\left( {\tan x - x} \right)dx = \tan 1 - 1 + \left( {\ln \left| {\cos x} \right| + \frac{{{x^2}}}{2}} \right)} \left| {_{\scriptstyle\atop\scriptstyle0}^{\scriptstyle1\atop\scriptstyle}} \right.\)

\( = \tan 1 + \ln \left( {\cos 1} \right) - \frac{1}{2}.\)

Chọn A.