Q. 26 - Calculus

Question

Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. 

$\int \frac{3}{x^2+1}dx$

Step-by-Step Solution

Answer

The answer is$3{\tan }^{-1}x+C\text{. }$

Step 1. Given Information.

The given integral is $\int \frac{3}{x^2+1}dx$.

Step 2. Integration.

On integrating,

$$\begin{gathered} \int \left(\frac{3}{x^2+1}\right)dx \\ =3\int \frac{1}{x^2+1}dx \\ =3{\tan }^{-1}x+C \end{gathered}$$

Step 3. Verification.

On differentiating $3{\tan }^{-1}x+C$, we get,

$=\frac{3}{1+x^2}$

Hence Proved.