Integrate the function: ^2(2x - 3) - Vidyadip

Question

Integrate the function: $\tan^2(2x - 3)$

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Answer

$\int {{{\tan }^2}\left( {2x - 3} \right)} dx$$ = \int {\left\{ {{{\sec }^2}\left( {2x - 3} \right) - 1} \right\}} dx$
$ = \int {{{\sec }^2}\left( {2x - 3} \right)} dx - \int {1dx} $
Using $\int {{{\sec }^2}\left( {ax + b} \right)} dx = \frac{{\tan \left( {ax + b} \right)}}{a} + c$
$= \frac{{\tan \left( {2x - 3} \right)}}{2} - x + c$

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