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

The integral of e^{-4ln(x)} is -1/(3x^3)+C

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integral of e^{-4ln(x)}

\int e^{- 4 l n (x)} d x

- \frac{1}{3 x ^{3}} + C

Solution steps

\int e^{- 4 l n (x)} d x

Simplify

e^{- 4 l n (x)} : \frac{1}{x ^{4}}

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

Apply the Power Rule

: - \frac{1}{3 x ^{3}}

= - \frac{1}{3 x ^{3}}

Add a constant to the solution

= - \frac{1}{3 x ^{3}} + C

(7 + x^{12}) \frac{d y}{d x} = x^{11} y

x \to - 4 lim (\frac{x}{x + 4})

x \to 3 - lim (- x^{2} + \frac{5}{2} x + 3)

\frac{d}{d x} (5 x^{4} sin^{3} (2 x))

\frac{d}{d x} (\frac{5 x ^{6} + 4 x ^{5} + 3 x ^{4}}{6 x ^{2}})

What is the integral of e^{-4ln(x)} ?
The integral of e^{-4ln(x)} is -1/(3x^3)+C