Can anybody show me the trick to doing the following integral? All of the examples in my book do this thing with common denominators that makes the integral much simpler to solve, but they basically skip the step in the examples, and leave you to figure it out for yourself. Integral to follow:

Question

theoreo · Answer

$$6\pi \int\limits_{3}^{7}\sqrt{x-3}*\sqrt{1+(\frac{ 9 }{ 4 }*\frac{ 1 }{ (x-3)}}$$

theoreo · Answer

For informational purposes, the correct answer is 49pi

anonymous · Answer

$$\sqrt{x-3}*\sqrt{1+\frac{ 9 }{ 4(x-3) }}=\sqrt{x-3}*\sqrt{\frac{ 4(x-3)+9 }{ 4(x-3) }}$$
$$=\sqrt{x-3}*\frac{ \sqrt{4x-3} }{ \sqrt{4(x-3)} }=\sqrt{x-3}\frac{ \sqrt{4x-3} }{ 2\sqrt{x-3} }$$

anonymous · Answer

And then you can get the sqrt(x-3) to cancel

theoreo · Answer

Ahhh I see. I was on that track, but I didn't simplify it enough. Thanks a lot.

anonymous · Answer

Sure, np :)