How do you find the antiderivative of ${(e^{- 2} x)}^{2}$ $(e^-2x)^2$ ?

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How do you find the antiderivative of ${(e^{- 2} x)}^{2}$ $(e^-2x)^2$ ?

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Answer 1 · 2017-02-03T12:28:21

$\int {(e^{- 2} x)}^{2} d x = \int e^{- 4} x^{2} d x = e^{- 4} \int x^{2} d x = e^{- 4} (\frac{x^{2 + 1}}{2 + 1})$ $int(e^-2x)^2dx=inte^-4x^2dx=e^-4intx^2dx=e^-4(x^(2+1)/(2+1))$

$= \frac{e^{- 4}}{3} x^{3} + C, or, \frac{x^{3}}{3 e^{4}} + C .$ $=(e^-4)/3x^3+C, or, x^3/(3e^4) +C.$

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How do you find the antiderivative of ${(e^{- 2} x)}^{2}$ $(e^-2x)^2$ ?

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