# Integral Qs

• Nov 22nd 2013, 04:27 PM
jonsanders
Integral Qs
Hi, I am trying to study for a math test and there are a couple of questions I don't understand.

1) How would I integrate (x3-x2+x-1)/(x2) dx? Could someone give me of an idea of what method I would use?

2) How would I use the substitution method to solve for (sqrt(lnx))/x? What would be my u? lnx or sqrt(lnx)?

3) How would I use substitution to integrate sin(3x)e(cos3x) dx?

Any help with any of these is greatly appreciated. Even knowing where to start would be great. Thanks!
• Nov 22nd 2013, 04:43 PM
HallsofIvy
Re: Integral Qs
Quote:

Originally Posted by jonsanders
Hi, I am trying to study for a math test and there are a couple of questions I don't understand.

1) How would I integrate (x3-x2+x-1)/(x2) dx? Could someone give me of an idea of what method I would use?

Start with basic algebra: \$\displaystyle \dfrac{x^3- x^2+ x- 1}{x^2}= \dfrac{x^3}{x^2}- \dfrac{x^2}{x^2}+ \dfrac{x}{x^2}- \dfrac{1}{x^2}= x- 1+ x^{-1}- x^{-2}\$

Quote:

2) How would I use the substitution method to solve for (sqrt(lnx))/x? What would be my u? lnx or sqrt(lnx)?
Did you consider trying both? If you let u= ln(x), what is du? If you let u= sqrt(ln(x)), what is du? Which works?

Quote:

3) How would I use substitution to integrate sin(3x)e(cos3x) dx?

Any help with any of these is greatly appreciated. Even knowing where to start would be great. Thanks!
Again, obvious substitutions are either u= 3x or u= cos(3x). What do you get for du if you try either of those?
• Nov 22nd 2013, 05:08 PM
jonsanders
Re: Integral Qs
Quote:

Start with basic algebra: \dfrac{x^3- x^2+ x- 1}{x^2}= \dfrac{x^3}{x^2}- \dfrac{x^2}{x^2}+ \dfrac{x}{x^2}- \dfrac{1}{x^2}= x- 1+ x^{-1}- x^{-2}
Wow, didn't think it would be that simple..

Quote:

Again, obvious substitutions are either u= 3x or u= cos(3x). What do you get for du if you try either of those?
I thought u would be the more complex part of the problem because how do you go from u=3x or u=cos(3x) to getting e involved?
• Nov 22nd 2013, 06:14 PM
Prove It
Re: Integral Qs
In order to use a substitution, you need to look for an "inner" function which you can let u be, and you need to check to see if this inner function's derivative is a factor (or at least, a constant multiple of a factor) in your integrand.