What is (e^x*(1/(x^2+1)))(xe^x) ?

The solution to (e^x*(1/(x^2+1)))(xe^x) is (e^{2x}x)/(x^2+1)

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simplify (e^x*(1/(x^2+1)))(xe^x)

simplify

(e^{x} \cdot (\frac{1}{x ^{2} + 1})) (x e^{x})

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

Solution steps

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{x} e^{x} = e^{x + x}

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

Add similar elements:

x + x = 2 x

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

Multiply fractions:

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

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

Multiply:

1 \cdot x = x

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

(4.3 \cdot 1 0^{- 3}) (14 \cdot 1 0^{- 3})

5.67 \cdot (1 0^{- 8})

(e^{- 0.1}) (e^{- 0.1})

(7.2 x 1 0^{- 7}) (6 x 1 0^{- 3})

\frac{5000 π}{0.3} \cdot 1 0^{- 7}

What is (e^x*(1/(x^2+1)))(xe^x) ?
The solution to (e^x*(1/(x^2+1)))(xe^x) is (e^{2x}x)/(x^2+1)