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Popular >

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

: \int \frac{1}{u ^{2}} d u

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

Apply the Power Rule

: - \frac{1}{u}

= \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

Popular Examples

integral of-2x^2+2x

\int - 2 x^{2} + 2 x d x

integral of (sqrt(x^2+x^{-2)+2})/x

\int \frac{x ^{2} + x ^{- 2} + 2}{x} d x

integral of (2x+7)^5

\int (2 x + 7)^{5} d x

integral of (3100)/(1+0.25x)

\int \frac{3100}{1 + 0.25 x} d x

integral of 12-x^2

\int 12 - x^{2} d x

Frequently Asked Questions (FAQ)

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