- #1
teneleven
- 12
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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?
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