What is the integral of e^{-1/2} ?

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

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integral of e^{-1/2}

\int e^{- \frac{1}{2}} d x

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

Solution steps

\int e^{- \frac{1}{2}} d x

Integral of a constant:

\int a d x = a x

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

Apply exponent rule:

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

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

Add a constant to the solution

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

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y^{^{''}} - y = 2 x e^{x}

\frac{\partial}{\partial v} (\frac{u}{v})

\frac{d}{d x} (5 + x)