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Integration by Parts of Fractions?

Hello I am revising for my maths exam and came across some questions I was unsure of:

a) x/e^x

b) ln4x / x^3


Thanks in advance for all the help
Original post by Peace&Love
Hello I am revising for my maths exam and came across some questions I was unsure of:

a) x/e^x

b) ln4x / x^3


Thanks in advance for all the help


1ex=e−x.\frac{1}{e^x} = e^{-x}.
Original post by brittanna
1ex=e−x.\frac{1}{e^x} = e^{-x}.



Yes does that mean x/e^x is xe^-x?
Original post by Peace&Love
Yes does that mean x/e^x is xe^-x?


Yes! And x^3 is similar.
Original post by brittanna
Yes! And x^3 is similar.


so does this mean the lnx question is

x^-3 ln4x?
Original post by Peace&Love
so does this mean the lnx question is

x^-3 ln4x?


Yep :biggrin:.
Original post by brittanna
Yep :biggrin:.



Thanks so much!
Original post by brittanna
Yep :biggrin:.


Just to confirm would the overall answer to part b be:

(-1/2)(x^-2)ln4x - (x^-2)/4

I haven't actually written my answer with brackets but just to make it clearer for you to see what I mean.
Original post by Peace&Love
Just to confirm would the overall answer to part b be:

(-1/2)(x^-2)ln4x - (x^-2)/4

I haven't actually written my answer with brackets but just to make it clearer for you to see what I mean.


Yeah, I think that's correct :biggrin:. Remember, a good way of checking your answer is to try differentiating it to see if you get back to what you started with.
Original post by brittanna
Yeah, I think that's correct :biggrin:. Remember, a good way of checking your answer is to try differentiating it to see if you get back to what you started with.



ok thank you. the answer in the book is -ln4x/2x^2 - 1/4x^2 is this the same thing. Sorry i get confused
Original post by Peace&Love
ok thank you. the answer in the book is -ln4x/2x^2 - 1/4x^2 is this the same thing. Sorry i get confused


Yeah, they're the same as x−2=1x2x^{-2} = \frac{1}{x^2}. Maybe if you write times symbols between each of the parts, it might help you see how the two answers are the same a bit more clearly :smile:.

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