What is e^{-(x^2-ln|x|+C)} ?

The solution to e^{-(x^2-ln|x|+C)} is (|x|)/(e^{x^2+C)}

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simplify e^{-(x^2-ln|x|+C)}

simplify

e^{- (x^{2} - l n ∣ x ∣ + C)}

\frac{∣ x ∣}{e ^{x^{2} + C}}

Solution steps

e^{- (x^{2} - l n ∣ x ∣ + C)}

Apply exponent rule:

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

= \frac{1}{e ^{(x^{2} - l n ∣ x ∣ + C)}}

Remove parentheses:

(a) = a

= \frac{1}{e ^{x^{2} - l n ∣ x ∣ + C}}

e^{x^{2} - l n ∣ x ∣ + C} = e^{x^{2} + C} ∣ x ∣^{- 1}

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

Multiply

∣ x ∣^{- 1} e^{x^{2} + C} : \frac{e ^{x^{2} + C}}{∣ x ∣}

= \frac{1}{\frac{e ^{x^{2} + C}}{∣ x ∣}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{∣ x ∣}{e ^{x^{2} + C}}

3 x (x e^{x})

(x) \cdot (y)

\frac{( 3 - x )}{( x ^{2} - 1 )}

What is e^{-(x^2-ln|x|+C)} ?
The solution to e^{-(x^2-ln|x|+C)} is (|x|)/(e^{x^2+C)}