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Popular >

integral of 1/(-e^x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

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

Substitute back

u = e^{x}

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

Simplify

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

Add a constant to the solution

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

Popular Examples

integral of (1+w)/(3-w^2)

\int \frac{1 + w}{3 - w ^{2}} d w

integral of 3/(1-cos(x))

\int \frac{3}{1 - cos ( x )} d x

integral of ln(2t+1)

\int ln (2 t + 1) d t

integral of ((-1)/x-ln(2)+1/(x^2))

\int (\frac{- 1}{x} - ln (2) + \frac{1}{x ^{2}}) d x

integral of 3/(x^2+14x+97)

\int \frac{3}{x ^{2} + 14 x + 97} d x

Frequently Asked Questions (FAQ)

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