Đáp án:
$\displaystyle\int\limits_0^{\tfrac{\pi}{4}}\tan^3xdx=\dfrac12-\dfrac12\ln2$
Giải thích các bước giải:
$\quad I =\displaystyle\int\limits_0^{\tfrac{\pi}{4}}\tan^3xdx$
$\Leftrightarrow I = \dfrac{\tan^2x}{2}\Bigg|_0^{\tfrac{\pi}{4}} - \displaystyle\int\limits_0^{\tfrac{\pi}{4}}\tan xdx$
$\Leftrightarrow I = \dfrac12+ \ln(\cos x)\Bigg|_0^{\tfrac{\pi}{4}}$
$\Leftrightarrow I = \dfrac12 - \dfrac12\ln2$
