#Integration by substitution exponential question

51 messages · Page 1 of 1 (latest)

stark pumice
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when we multiply du with the integral i dont see how it can turn into that

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steady stratus
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@stark pumice

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are u talking about the 3rd line

stark pumice
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im talking about the first line under the table they gave

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i understand how dx equals that

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shouldnt the numerator be to the power of 4 since the denominator is e^4x

steady stratus
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i think they skipped some steps

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there must have been some simplifying involved to get that

stark pumice
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yeah they did, its confused the heck out of me

steady stratus
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alr lets work from the dx part

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e^4x /e^x - 2 2u/ u^2 + 2 du

stark pumice
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yes

steady stratus
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(u+2)^2 = e^x so e^4x = (u+2)^8

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e^x - 2 is just u

stark pumice
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wait hold up

steady stratus
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yea

stark pumice
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isnt e^x-2 = u^2??

steady stratus
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yh

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i made e^x the subject

stark pumice
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so surely it would be (u^2+2)^4

steady stratus
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oh shit mb

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what am i doing lol

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yh ur right

stark pumice
stark pumice
steady stratus
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mb made a mistake

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so u^2 + 2)^4 is e^4x

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right

stark pumice
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okay so

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then we multiply that by 2u

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and the denominator is u^2 and we multiply that by u^2+2

steady stratus
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u^2 + 2)^4 / u^2 2u/u^2 + 2 du

stark pumice
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yes

steady stratus
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there'll be some cancelling with the u^2 and 2u

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and the u^2 + 2 and u^2 + 2)^4

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which gets you
(u^2 + 2)^3 / u 2 du

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2(u^2 + 2)^3 / u du

stark pumice
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OHHHH

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that makes a bunch of sense

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i went wrong with the cancelling

steady stratus
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u sub is kinda weird ngl

stark pumice
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thank you so much @steady stratus

steady stratus
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np

stark pumice
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you're the goat

steady stratus
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far from it

stark pumice
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legit spent 10 mins just staring at the solution 😭

stark pumice
steady stratus
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lmao yh the solution banks are annoying

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they miss out the vital shit

stark pumice
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thanks bro

stark pumice