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July 30, 2014

July 30, 2014

Posted by **Nikki** on Saturday, October 23, 2010 at 7:31pm.

Use the indicated substitution (above) to evaluate the integral. Confirm answer by differentiation.

Okay, so I found that du/dx is 1/3. dx is 3du. Just by looking at the integral I can tell this is some form of tan^-1(x), if we change it to int(1/(x^2+9) * dx). Thing is, I don't really know where to put in u to make this work. Help please???

Thank you!

- Calculus -
**MathMate**, Saturday, October 23, 2010 at 8:27pmu=x/3

du = (1/3)dx

dx = 3du

x²=9u²

Substitute in the integral to get:

∫ dx/(x²+9)

=∫ 3du/(9u²+9)

=∫ (1/3)du/(x²+1)

Can you take it from here, using your tan^{-1}suggestion?

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