What is 5t^2e^{-10t}dt ?

The solution to 5t^2e^{-10t}dt is (5t^2dt)/(e^{10t)}

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simplify 5t^2e^{-10t}dt

simplify

5 t^{2} e^{- 10 t} d t

\frac{5 t ^{2} d t}{e ^{10 t}}

Solution steps

5 t^{2} e^{- 10 t} d t

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= 5 \cdot \frac{1}{e ^{10 t}} t^{2} d t

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 5 t ^{2} d t}{e ^{10 t}}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5 t ^{2} d t}{e ^{10 t}}

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