Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

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integration by parts - WHAT AM I DOING WRONG

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:

:facepalm2:

. i've made a similar mistake on similar questions too

The derivative of ln(3x) is just 1/x. Because ln(3x) = ln 3 + ln x, with ln 3 being a constant.

By the chain rule,

u = \ln 3x \Rightarrow \dfrac{du}{dx} = \dfrac{1}{3x}\times 3 = \dfrac{1}{x}

<-- that's your problem

OP

omfg

:facepalm2:

yeah

kimoso

omfg

:facepalm2:

yeah

Lol at this :p:

:p:

Stick to languages kimoso, anyway how are you doing with your exams? Had the Dutch yet? :smile:

:smile:

OP

win2kpro

Lol at this :p:

:p:

Stick to languages kimoso, anyway how are you doing with your exams? Had the Dutch yet? :smile:

:smile:

nope, that is my last exam! what about you?

kimoso

nope, that is my last exam! what about you?

Ooh long wait :p:

:p:

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

:wink:

Lets just hope im as happy with the results :smile:

:smile:

Good luck with your exams!!

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