What is the integral from 1 to 5 of (3t)/(e^{2t)} ?

The integral from 1 to 5 of (3t)/(e^{2t)} is 3(-(11)/(4e^{10)}+3/(4e^2))

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integral from 1 to 5 of (3t)/(e^{2t)}

\int_{1}^{5} \frac{3 t}{e ^{2 t}} d t

3 (- \frac{11}{4 e ^{10}} + \frac{3}{4 e ^{2}})

Decimal Notation

0.30412 \dots

Solution steps

\int_{1}^{5} \frac{3 t}{e ^{2 t}} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{1}^{5} \frac{t}{e ^{2 t}} d t

Apply Integration By Parts

: [- \frac{1}{2} e^{- 2 t} t - \int - \frac{1}{2} e^{- 2 t} d t]_{1}^{5}

= 3 [- \frac{1}{2} e^{- 2 t} t - \int - \frac{1}{2} e^{- 2 t} d t]_{1}^{5}

\int - \frac{1}{2} e^{- 2 t} d t = \frac{1}{4} e^{- 2 t}

= 3 [- \frac{1}{2} e^{- 2 t} t - \frac{1}{4} e^{- 2 t}]_{1}^{5}

Compute the boundaries:

- \frac{11}{4 e ^{10}} + \frac{3}{4 e ^{2}}

= 3 (- \frac{11}{4 e ^{10}} + \frac{3}{4 e ^{2}})

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What is the integral from 1 to 5 of (3t)/(e^{2t)} ?
The integral from 1 to 5 of (3t)/(e^{2t)} is 3(-(11)/(4e^{10)}+3/(4e^2))