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Question
\[\int\limits_0^{\pi/4} \tan^4 x dx\]
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Solution
\[\int_0^\frac{\pi}{4} \tan^4 x d x\]
\[ = \int_0^\frac{\pi}{4} \tan^2 x\left( se c^2 x - 1 \right) d x\]
\[ = \int_0^\frac{\pi}{4} \tan^2 x se c^2 x dx - \int_0^\frac{\pi}{4} \tan^2 x dx\]
\[ = \left[ \frac{\tan^3 x}{3} \right]_0^\frac{\pi}{4} - \left[ \tan x - x \right]_0^\frac{\pi}{4} \]
\[ = \frac{1}{3} - 1 + \frac{\pi}{4}\]
\[ = \frac{\pi}{4} - \frac{2}{3}\]
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