Calculus Examples

$\frac{1}{e^{- x}}$

Step 1

Simplify the expression.

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Step 1.1

Negate the exponent of $e^{- x}$ and move it out of the denominator.

$\int 1 {(e^{- x})}^{- 1} d x$

Step 1.2

Simplify.

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Step 1.2.1

Multiply the exponents in ${(e^{- x})}^{- 1}$ .

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Step 1.2.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\int 1 e^{- x \cdot - 1} d x$

Step 1.2.1.2

Multiply $- x \cdot - 1$ .

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Step 1.2.1.2.1

Multiply $- 1$ by $- 1$ .

$\int 1 e^{1 x} d x$

Step 1.2.1.2.2

Multiply $x$ by $1$ .

$\int 1 e^{x} d x$

Step 1.2.2

Multiply $e^{x}$ by $1$ .

$\int e^{x} d x$

Step 2

The integral of $e^{x}$ with respect to $x$ is $e^{x}$ .

$e^{x} + C$