Integral

**javax** · September 17th 2008, 03:12 PM

Hello!

$<br /> \int{\frac{xdx}{(x^2-3x+2)\sqrt{x^2-4x+3}}}<br />$

Haven't been much familiar with these, so I need some help!
I think there's a hint but but I'm not sure if it's right: $\sqrt{(x-1)(x-3)}=t(x-3)$ , anyway I don't know how to use it!

Thanks

**shawsend** · September 17th 2008, 05:11 PM

Alright, then make the substitution $t=\frac{\sqrt{(x-1)(x-3)}}{x-3}=\sqrt{\frac{x-1}{x-3}}$ . Solve for x, calculate $dx$ in terms of $dt$ , then substitute everything in the integral in terms of t. When I do that I get $\int \frac{3t^2-1}{t^2+t^4}dt$ . Integrate, then bring everything back to x.

**javax** · September 17th 2008, 05:23 PM

Ok thanks. One more question, Is there any order how to make these substitutions or we just have to be vigilant?

Thanks

**Chop Suey** · September 17th 2008, 05:49 PM

You may have to experiment abit. Try a substitution here and there, and if it looks like a deadend to you, try another one. With practice, you will learn to see what substitutions to make on the go. Sometimes you may need to use integration by parts rather than substitution.

Thread: Integral

LinkBack

Thread Tools

Display

Integral

Similar Math Help Forum Discussions

Use Cauchy's integral theorem for derivatives to evaluate the contour integral.

Graph the region of integration and evaluate the double integral (integral from 0 to

Explaining result: comparing line integral and two-form integral

write [integral of] dx/SQRT(sinx) in terms of an elliptic integral

Evaluating a double integral to find its signle integral.

Search Tags