What is the integral of e^{-X} ?

The integral of e^{-X} is -e^{-X}+C

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integral of e^{-X}

\int e^{- X} d X

- e^{- X} + C

Solution steps

\int e^{- X} d X

Apply u-substitution

: \int - e^{u} d u

= \int - e^{u} d u

Take the constant out:

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

= - \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - e^{u}

Substitute back

u = - X

= - e^{- X}

Add a constant to the solution

= - e^{- X} + C

\int 3 + csc (x) \cdot cot (x) d x

f (x) = \frac{1 + x}{1 + e ^{x}}

f (x) = sec^{3} (x)

2 \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 3 y = 0

n = 0 \sum \infty 83 (\frac{1}{100})^{n}