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Popular Calculus >

integral of 2/(e^t)

Solution

\int \frac{2}{e ^{t}} d t

Solution

- \frac{2}{e ^{t}} + C

Solution steps

\int \frac{2}{e ^{t}} d t

Take the constant out:

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

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

Apply u-substitution

= 2 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

= 2 (- \frac{1}{u})

Substitute back

u = e^{t}

= 2 (- \frac{1}{e ^{t}})

Simplify

2 (- \frac{1}{e ^{t}}) : - \frac{2}{e ^{t}}

= - \frac{2}{e ^{t}}

Add a constant to the solution

= - \frac{2}{e ^{t}} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 2/(e^t) ?
The integral of 2/(e^t) is -2/(e^t)+C