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

The integral of e^{-4}x is (x^2)/(2e^4)+C

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integral of e^{-4}x

integral

e^{- 4} x

\frac{x ^{2}}{2 e ^{4}} + C

Solution steps

\int e^{- 4} x d x

Take the constant out:

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

= e^{- 4} \cdot \int x d x

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

Apply the Power Rule

: \frac{x ^{2}}{2}

= \frac{1}{e ^{4}} \cdot \frac{x ^{2}}{2}

Simplify

\frac{1}{e ^{4}} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{2 e ^{4}}

= \frac{x ^{2}}{2 e ^{4}}

Add a constant to the solution

= \frac{x ^{2}}{2 e ^{4}} + C

\frac{4 x}{( x ^{2} + 1 )}

cosh^{2} (x)

1 - cot^{2} (x)

\frac{- 2}{x ^{3}}

\frac{ln ( x ^{2} )}{x ^{3}}