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<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>
<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>

substitution integration of x(2x^2 -5)dx, u=2x^2 -5

how do you get to the answer of 1/6 (2x^2-5)^3/2 +c from integration by substitution of x(2x^2 -5)dx, u=2x^2 -5

do you have a specific set of steps that you use when working with these substitution integration questions?

i don't see the use of rearranging dx because i get 4x/du=dx or du=4xdx
what do you do with either of them. are they even correct. if so, which one is correct and how do you know?
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KoDang
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KoDang
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You need to go over integration by sub with your teacher because god knows what method you have used to get 1/6 (2x^2-5)^3/2 +c
Original post by esmeralda123
how do you get to the answer of 1/6 (2x^2-5)^3/2 +c from integration by substitution of x(2x^2 -5)dx, u=2x^2 -5

do you have a specific set of steps that you use when working with these substitution integration questions?

i don't see the use of rearranging dx because i get 4x/du=dx or du=4xdx
what do you do with either of them. are they even correct. if so, which one is correct and how do you know?


I assume you mean ∫x(2x2−5)1/2dx\int x(2x^2-5)^{1/2}dx

So then u=2x2−5u=2x^2-5, SUBSTITUTE that in, and clearly also we have du=4xdxdu=4x dx

What do you do with either of them? Well with the current form, you want to rearrange for dx and SUBSTITUTE that for dx in the integral. The leftover xx cancel and you're left with a power of uu to integrate which is trivial. Once you integrate, replace u's with 2x2−52x^2-5 and there's your answer.
(edited 6 years ago)

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