Integration Questions

[Mears]

What are the methods of integration for the following:

1. xe^x = (x-1)e^x

2. 1/x^2

Not integration but how does xln(2x) - xlnx = ln2? I thought it would be xlnx.

 

[sohcrates]

well, for #2, make 1/x^2 into x^-2 and then itegration becomes trivial

 

[Mears]

Good call, I feel like a retard now. I wish I would've retained some of the information from calc 1 and 2. Argggg....

 

[yoyo25]

For the first one, you would use integration by parts..like set u = x, and dv = e^x or vice versa and solve for u*v - int(v*du) or something like that...

 

[sohcrates]

here's what i think for the last one:

x(Ln2x-Lnx) = xLn(2x/x) = XLn2

therefore, i think it equals Xln2, NOT Ln2

 

[Random Variable]

1. Integral (x*e^x)dx

u= x
du= dx
dv=e^x
v=e^x

x*e^x - Integral (e^x)dx
= x*e^x-e^x = e^x(x-1) + C

2) Integral (1/x^2)dx

x^(-2+1)/-1 = -1/x +C

3) x(ln2x-lnx)= x*ln(2x/x)= x*ln2

 

[yoyo25]

I hope we didn't just do your homework for you! You should really attempt these problems, they are really no that difficult....they are what you call "model" problems...every calc book probably uses these "exact" questions in their examples section.

 

[Mears]

No you didn't just do my homework for me. My homework is based on the concept of integrals of multivariable functions. Those integrals were only small parts of a few of the problems. I already had the answers since I am supplied with an integral table, but I wanted to remember the methods of how they are reached and for #3 it's a good thing I asked because the solution listed was wrong.