Chapter 5: Q 31. (page 452)

Solve the following integral.
$\int s e c^{3} 2 x d x$

Short Answer

Expert verified

Answer is $\frac{\tan 2 x s e c 2 x}{4} + \frac{\ln [\tan (\frac{π}{4} + x)]}{4} + C$

Step by step solution

Step 1. Given information

An integral is $\int s e c^{3} 2 x d x$

Step 2. Explanation

Let $u = 2 x$

$\begin{array}{rcl} \int s e c^{3} 2 x d x & = & \frac{1}{2} \int s e c^{3} u d u \\ = & \frac{1}{2} [s e c u \tan u - \int \tan u \tan u s e c u d u] \\ = & \frac{\tan u s e c u}{4} + \frac{\ln [\tan (\frac{π}{4} + \frac{u}{2})]}{4} + C \\ = & \frac{\tan 2 x s e c 2 x}{4} + \frac{\ln [\tan (\frac{π}{4} + x)]}{4} + C \end{array}$

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Solve the following integral.
$\int s e c^{3} 2 x d x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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Solve the following integral.
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