What is e^{-x}((x^2)/2+x+c) ?

The solution to e^{-x}((x^2)/2+x+c) is (x^2+2x+2c)/(2e^x)

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simplify e^{-x}((x^2)/2+x+c)

simplify

e^{- x} (\frac{x ^{2}}{2} + x + c)

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

Solution steps

e^{- x} (\frac{x ^{2}}{2} + x + c)

Apply exponent rule:

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

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

Multiply fractions:

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

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

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

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

Join

\frac{x ^{2}}{2} + x + c : \frac{x ^{2} + 2 x + 2 c}{2}

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

Apply the fraction rule:

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

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

(1.24 x 1 0^{2}) x (4 x 1 0^{- 2})

x - 6 \cdot 6 - x

(8 a^{3} b^{4}) (9 ab)

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