- #1

- 12

- 0

## Homework Statement

[tex]\int\frac{x^3}{\sqrt{x^2 + 9}}[/tex]

## Homework Equations

[tex]x = 3\tan{\theta}[/tex]

[tex]dx=3\sec^2{\theta}[/tex]

## The Attempt at a Solution

[tex]27\int\tan^3{\theta}\sec{\theta}[/tex]

[tex]27\int\tan{\theta}(\sec^2{\theta} - 1)\sec{\theta}[/tex]

[tex]27\int(sec^3{\theta} - \sec{\theta})\tan{\theta}[/tex]

[tex]27[\int\sec^3{\theta}\tan{\theta} - \int\sec{\theta}\tan{\theta}[/tex]

[tex]27(\frac{1}{3}\sec^3{\theta} - \sec{\theta})[/tex]

[tex]= 27[\frac{1}{3}(\frac{\sqrt{x^2 + 9}}{3})^3 - \frac{\sqrt{x^2 + 9}}{3}] + C[/tex]

The correct answer is as follows:

[tex]\frac{1}{3}(x^2 - 18)\sqrt{x^2 + 9}[/tex]Any ideas?

Last edited: