Evaluate the definite integral exactly \int^1_0 (e^(5x)-5x)^3(e^(5x)-1)dx

kramtus51

kramtus51

Answered question

2022-01-04

Evaluate the definite integral exactly
01(e5x5x)3(e5x1)dx

Answer & Explanation

Steve Hirano

Steve Hirano

Beginner2022-01-05Added 34 answers

Given
01(e5x5x)3(e5x1)dx
[Let t=e5x5xdtdx=e5x(5)5dtdx=5(e5x1)dt5=e5x1dx] and [x=0t=e5(0)5(0)t=1x=1t=e5(1)5(1)t=e55]
01(e5x5x)3(e5x1)dx=t=1e55t3dt5
=15[t44]t=1e55
=15[(e55)44(1)44]
=120[(e55)41]

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