Easy integral problem

**virtuoso735** · March 26th 2009, 06:59 AM

How do you find the integral of sqrt[1+81x]? u-substitution and integration by parts does not seem to work.

**Danny** · March 26th 2009, 07:02 AM

Originally Posted by virtuoso735

How do you find the integral of sqrt[1+81x]? u-substitution and integration by parts does not seem to work.

It should $\int\sqrt{1+81x}\,dx$ . Let $u = 1 + 81x$ . Your problem reduce to $\frac{1}{81} \int \sqrt{u}\, du$

**Chop Suey** · March 26th 2009, 07:03 AM

On the contrary, u-sub does work. Try $u = 1+81x$

But for such a trivial integral, it's best to see it as $\frac{1}{81} \int \sqrt{1+81x}~d(1+81x)$ and integrate directly.

Are you sure you did not mean $\sqrt{1+81x^2}$ instead?

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