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Question
\[\int \tan^{3/2} x \sec^2 \text{x dx}\]
Sum
Solution
\[\int \tan^\frac{3}{2} x \cdot \sec^2 \text{x dx}\]
\[Let \tan x = t\]
\[ \Rightarrow \sec^2 x = \frac{dt}{dx}\]
\[ \Rightarrow \sec^2 \text{x dx} = dt\]
\[Now, \int \tan^\frac{3}{2} x \cdot \sec^2 \text{x dx} \]
\[ = \int t^\frac{3}{2} dt\]
` = [t^{3/2 +1}/{3/2+1}] + C`
\[ = \frac{2}{5} t^\frac{5}{2} + C\]
\[ = \frac{2}{5} \tan^\frac{5}{2} x + C\]
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