Chapter 7.2, Problem 44E

To determine

To determine the integral ${\displaystyle \int \frac{1}{\sqrt{5x+8}}dx}$ by substitution.

Answer to Problem 44E

The value of the integral ${\displaystyle \int \frac{1}{\sqrt{5x+8}}dx}$ is $\frac{2{\left(5x+8\right)}^{1/2}}{5}+C$

Explanation of Solution

Given information: ${\displaystyle \int \frac{1}{\sqrt{5x+8}}dx}$

Formula used: ${\displaystyle \int x^{n}dx=\frac{x^{n+1}}{n+1}+C}$

Calculation :

The given integral becomes as:

  ${\displaystyle \int {\left(5x+8\right)}^{-1/2}dx}=\frac{{\left(5x+8\right)}^{1/2}}{(5)(1/2)}+C$

Hence, ${\displaystyle \int \frac{1}{\sqrt{5x+8}}dx}=\frac{2{\left(5x+8\right)}^{1/2}}{5}+C$