What is the integral of e^{-4x} ?

The integral of e^{-4x} is -1/4 e^{-4x}+C

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integral of e^{-4x}

\int e^{- 4 x} d x

- \frac{1}{4} e^{- 4 x} + C

Solution steps

\int e^{- 4 x} d x

Apply u-substitution

: \int - \frac{1}{4} e^{u} d u

= \int - \frac{1}{4} e^{u} d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{4} e^{u}

Substitute back

u = - 4 x

= - \frac{1}{4} e^{- 4 x}

Add a constant to the solution

= - \frac{1}{4} e^{- 4 x} + C

\int \frac{( x ^{10} )}{x ^{2} + x - 2} d x

f (x) = \frac{4}{x}, at x = 3

\frac{1}{4 s ^{2} + 1}

x \to 0 lim (x^{2} cos (\frac{2}{x}))

x \to - 4 lim (∣ x + 4 ∣)