Use integration by parts to prove the reduction formula. int x^n e^x dx=x^n e^x -n int x^(n-1)e^x dx

klepkowy7c 2022-07-28 Answered
Use integration by parts to prove the reduction formula.
x n e x d x = x n e x n x n 1 e x d x
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Answers (1)

Brenton Gay
Answered 2022-07-29 Author has 13 answers
consider:
[ x n e x ] = x n e x + n x n 1 e x
x n e x = [ x n e x ] n x n 1 e x
x n e x d x = [ ( x n e x ) n x n 1 e x ] d x
= x n e x n x n 1 e x d x
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