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Popular >

integral of e/(e^x)

Solution

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

Solution

- e^{1 - x} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

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

Substitute back

u = e^{x}

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

Simplify

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

= - e^{1 - x}

Add a constant to the solution

= - e^{1 - x} + C

Graph

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\int (2 x + e^{y}) d x

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\int cos (5 - 7 x) d x

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\int sin (\frac{nπ x}{20}) d x

integral of (sec^2(θ)tan^3(θ))

\int (sec^{2} (θ) tan^{3} (θ)) d θ

integral of 3/(sqrt(x+1)+\sqrt{x)}

\int \frac{3}{x + 1 + x} d x

Frequently Asked Questions (FAQ)

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