integration by parts - WHAT AM I DOING WRONG Watch

frogout
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#1
Report Thread starter 9 years ago
#1
okay yeah so there is this question it is all "integrate x5ln3x" so i'm like okay i shall integrate this by parts and go

u=ln3x
du/dx= 1/3x

dv/dx=x5
v=x6/6

SO THEN i do

1/6x6ln3x - (the integral of) (1/6x6*1/3x=1/18x5)

= 1/6x6ln3x - 1/108x6 + k

HOWEVER the actual answer is
1/36x6(6ln3x-1)+k

so wherrrre am i going wrong? i know i'm probably making a stupid mistake somewhere, but i cant figure it out :facepalm2:. i've made a similar mistake on similar questions too
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Glutamic Acid
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#2
Report 9 years ago
#2
The derivative of ln(3x) is just 1/x. Because ln(3x) = ln 3 + ln x, with ln 3 being a constant.
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nuodai
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By the chain rule, u = \ln 3x \Rightarrow \dfrac{du}{dx} = \dfrac{1}{3x}\times 3 = \dfrac{1}{x} <-- that's your problem
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frogout
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#4
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omfg :facepalm2: yeah
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win2kpro
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#5
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(Original post by kimoso)
omfg :facepalm2: yeah
Lol at this :p: Stick to languages kimoso, anyway how are you doing with your exams? Had the Dutch yet?
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frogout
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(Original post by win2kpro)
Lol at this :p: Stick to languages kimoso, anyway how are you doing with your exams? Had the Dutch yet?
nope, that is my last exam! what about you?
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win2kpro
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(Original post by kimoso)
nope, that is my last exam! what about you?
Ooh long wait :p:

Dutch was my first exam! It went very well, im very happy about it

Lets just hope im as happy with the results

Good luck with your exams!!
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