Chapter 7.5, Problem 9E

To determine

To evaluate the integral

Answer to Problem 9E

The value of ${\displaystyle \int \frac{2}{x^2+1}}dx=2{\tan }^{-1}x+C$

Explanation of Solution

Given information:

The integral is ${\displaystyle \int \frac{2}{x^2+1}}dx$

Calculation:

The integral is ${\displaystyle \int \frac{2}{x^2+1}}dx$

Since ${\displaystyle \int \frac{1}{1+x^2}}dx={\tan }^{-1}x+C$

  ${\displaystyle \int \frac{2}{x^2+1}}dx=2{\displaystyle \int \frac{1}{x^2+1}}dx=2{\tan }^{-1}x+C\text{ , where }C\text{ is constant}$

Therefore, the value of ${\displaystyle \int \frac{2}{x^2+1}}dx=2{\tan }^{-1}x+C$