What is e^{-x^2}sqrt(1+4e^{-2x^2)x^2} ?

The solution to e^{-x^2}sqrt(1+4e^{-2x^2)x^2} is (sqrt(4e^{-2x^2)x^2+1})/(e^{x^2)}

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simplify e^{-x^2}sqrt(1+4e^{-2x^2)x^2}

simplify

e^{- x^{2}} 1 + 4 e^{- 2 x^{2}} x^{2}

\frac{4 e ^{- 2 x^{2}} x ^{2} + 1}{e ^{x^{2}}}

Solution steps

e^{- x^{2}} 1 + 4 e^{- 2 x^{2}} x^{2}

Apply exponent rule:

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

= \frac{1}{e ^{x^{2}}} 4 e^{- 2 x^{2}} x^{2} + 1

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Multiply:

1 \cdot 1 + 4 e^{- 2 x^{2}} x^{2} = 1 + 4 e^{- 2 x^{2}} x^{2}

= \frac{1 + 4 e ^{- 2 x^{2}} x ^{2}}{e ^{x^{2}}}

\frac{1}{2 π} e^{- \frac{x}{2}}

v f - 2 (2 m s^{2}) (300 m)

(e^{\frac{1}{2} x} ln (x)) (x e^{\frac{1}{2} x})

120 π \cdot 5 \cdot 1 0^{- 3}

24 x^{2} (a - x)^{2}

What is e^{-x^2}sqrt(1+4e^{-2x^2)x^2} ?
The solution to e^{-x^2}sqrt(1+4e^{-2x^2)x^2} is (sqrt(4e^{-2x^2)x^2+1})/(e^{x^2)}