brain freeze on indef. integral of sqrt[4 + 9x^2] dx

[quazzimotto]

Seems like this should be easier, but I'm running on empty w/studying for finals.

I was thinking trig sub but seems I need dx seperated in the numerator or U-sub, just stumped on starting this one. You can see what I was tryig to start, i think I need some zzz.

Yes, this is much smaller image... lol

http://home.comcast.net/~0server0/indef.jpg

I don't think I can use U-sub or trig sub for a radical in the numerator?

thanks

 

[galactus]

Let \(\displaystyle \L\\x=\frac{2}{3}tan({\theta}), \;\ dx=\frac{2}{3}sec^{2}({\theta})d{\theta}\)

\(\displaystyle \L\\\int\sqrt{4+9x^{2}}dx\)

\(\displaystyle \L\\\int\sqrt{4+9(\frac{4}{9}tan^{2}({\theta}))}\cdot\frac{2}{3}sec^{2}({\theta})d{\theta}\)

\(\displaystyle \L\\\int\sqrt{4(1+tan^{2}({\theta}))}\cdot\frac{2}{3}sec^{2}({\theta})d{\theta}\)

Now finish?.