What is the integral of e^{-3ln(x)} ?

The integral of e^{-3ln(x)} is -1/(2x^2)+C

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integral of e^{-3ln(x)}

\int e^{- 3 l n (x)} d x

- \frac{1}{2 x ^{2}} + C

Solution steps

\int e^{- 3 l n (x)} d x

Simplify

e^{- 3 l n (x)} : \frac{1}{x ^{3}}

= \int \frac{1}{x ^{3}} d x

Apply the Power Rule

= - \frac{1}{2 x ^{2}}

Add a constant to the solution

= - \frac{1}{2 x ^{2}} + C

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

\frac{d}{d x} (3 - x)

\int \frac{1}{8 + x ^{2}} d x

\int_{5}^{- 5} \frac{1}{∣ x ∣ ^{(\frac{2}{3})}} d x

n = 0 \sum \infty \frac{ln ( n )}{n !}

What is the integral of e^{-3ln(x)} ?
The integral of e^{-3ln(x)} is -1/(2x^2)+C