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Popular Calculus >

integral of 1/(3e^x)

Solution

\int \frac{1}{3 e ^{x}} d x

Solution

- \frac{1}{3 e ^{x}} + C

Solution steps

\int \frac{1}{3 e ^{x}} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int \frac{1}{e ^{x}} d x

Apply u-substitution

= \frac{1}{3} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

= \frac{1}{3} (- \frac{1}{u})

Substitute back

u = e^{x}

= \frac{1}{3} (- \frac{1}{e ^{x}})

Simplify

\frac{1}{3} (- \frac{1}{e ^{x}}) : - \frac{1}{3 e ^{x}}

= - \frac{1}{3 e ^{x}}

Add a constant to the solution

= - \frac{1}{3 e ^{x}} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 1/(3e^x) ?
The integral of 1/(3e^x) is -1/(3e^x)+C