Reduction Formula for x^n exp(ax)

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Calculus: We show the reduction formula for int x^n exp(ax) dx using integration by parts and apply it to find int (x+1)^2 exp(2x) dx. We also note that the formula works for definite integrals.
  1. MathDoctorBob
  2. Mathematics
  3. calculus
  4. integration
  5. parts
  6. reduction
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Комментарии
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just got this in my coursework, legend

doctorisjoe
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I didn't know Dwayne Johnson did calculus tutorials.

cliffordwilliams
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Good time of day! Is it possible to solve this integral, when n<0?

КириллФилатов-рр
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Thanks for that Bob. 
I see also that step 2 expansion  (see time 6.06) could have been fully ignored if the more complex expression 3 is evaluated first as one of the terms in it becomes half of term 2. (Seems like a good general rule to save effort)
Otherwise the reductions and the proof is just wonderful as it is building on the simple/basic block (u*v)' =u*v' +u'*v, something that also us rusty still recall.
Thanks again!

stenbjorsell
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@ian559fresno You're welcome! Integration by parts is usually Calculus 2. I normally skip these, but someone requested it. - Bob

MathDoctorBob
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@alullabyofpain I was leveling up when leveling up was a new thing (videogames and D&D). :) Bob

MathDoctorBob
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Is this the only method?
I’m trying to solve [x^4]*[e^x] but I’d like to find something faster than integration by parts

SuperMrlokito
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@candamohcine You're welcome! Hope things are good with you. - Bob

MathDoctorBob
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Is this Calculus 1 or 2 material? Thanks

ianfresno
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so this is the exp i need to level up? xD

alullabyofpain