Chapter 7.2, Problem 43E

To determine

To determine the integral ${\displaystyle \int \frac{1}{\cot 3x}dx}$ by substitution.

Answer to Problem 43E

The value of the integral ${\displaystyle \int \frac{1}{\cot 3x}dx}$ is $\frac{{\sec }^{2}3x}{3}+C$

Explanation of Solution

Given information: ${\displaystyle \int \frac{1}{\cot 3x}dx}$

Formula used: ${\displaystyle \int \tan (ax)dx=\frac{{\sec }^2(ax)}{a}+C}$

Calculation :

The given integral becomes as:

  ${\displaystyle \int \tan 3xdx}=\frac{{\sec }^{2}3x}{3}+C$

Hence, ${\displaystyle \int \frac{1}{\cot 3x}dx}=\frac{{\sec }^{2}3x}{3}+C$