Chapter 7.2, Problem 30E

To determine

To evaluate the integral .

Answer to Problem 30E

The value of the ${\displaystyle \int 3{\left(\sin x\right)}^{-2}dx}=-3\cot x+C$

Explanation of Solution

Given information:

The integral is ${\displaystyle \int 3{\left(\sin x\right)}^{-2}dx}$

Calculation:

The integral is ${\displaystyle \int 3{\left(\sin x\right)}^{-2}dx}$

  $\begin{array}{l}{\displaystyle \int 3{\left(\sin x\right)}^{-2}dx}\\ 3{\displaystyle \int \frac{1}{{\sin }^{2}x}}dx=3{\displaystyle \int \cos e{c}^2}xdx=-3\cot x+C,\text{where C is constant}\end{array}$

Hence ,the value of the ${\displaystyle \int 3{\left(\sin x\right)}^{-2}dx}=-3\cot x+C$ .