Integration by Parts

[anto]

Hi, well I'm having some trouble on some integration by parts homework. I can't figure out how to integrate

e^(root x), it will be of great help if you guys could give me some hints here, like what u or v are etc.

[Jay-qu]

are you told to do it by parts or can you use any method?

[anto]

well this is for a presentation i need to make in which I need to create 4 problems with their respective answers (and procedure to get the answer). This problem is straight from the integration by parts section of the book though so it should be solvable that way

[Nootropic]

what do you mean by "e^(root x)", that's relatively general and could have a lot of interpretations.

[Jay-qu]

he means

[math] \int{e^{\sqrt{x}}}dx[/math]

[anto]

yup thats it

[ronthepon]

It's possile that you've got to express sqrt(x) at 't' or something, and since that develops another constant nearby, you can integerate by parts.

 

Try taking [math]\sqrt{x}[/math] as t. I think that'll do it.

[anto]

yeah it should work, I'm going to try and post some steps here so you guys can correct me if i make a mistake.

t = root x

dt = 1/2root x dx

when I replace dt for dx my integral would now look like:

 

e^t (2 root x) dt then I need to replace root x for t

e^t (2t) dt

Integration by Parts = uv - (integral of )vdu

u = 2t dv = e^t dt

du = 2dt v = e^t

 

2t (e^t) - 2e^t

2e^t ( t - 1)

 

Substituting:

2e^root x ( rootx-1)

 

Please post some comments/corrections :)

[max4236]

differentiate (2e^rootx)*(rootx-1)

 

[2(rootx-1)*e^rootx]'

2(rootx-1)*(e^rootx)' + (2(rootx-1))'*e^rootx

[ 2(rootx-1)*e^rootx*1/(2rootx) ]+[2/(2rootx) * e^rootx]

e^rootx * [(rootx-1)/rootx+ 1/rootx]

e^rootx * [1-1/rootx+1/rootx]

e^rootx

 

yep, looks good