What is the integral of 100e^{-(x/(200))^2}*x ?

The integral of 100e^{-(x/(200))^2}*x is -2000000e^{-(x^2)/(40000)}+C

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integral of 100e^{-(x/(200))^2}*x

\int 100 e^{- (\frac{x}{200})^{2}} \cdot x d x

- 2000000 e^{- \frac{x ^{2}}{40000}} + C

Solution steps

\int 100 e^{- (\frac{x}{200})^{2}} x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 100 \cdot \int e^{- (\frac{x}{200})^{2}} x d x

Simplify

e^{- (\frac{x}{200})^{2}} x : e^{- \frac{x ^{2}}{40000}} x

= 100 \cdot \int e^{- \frac{x ^{2}}{40000}} x d x

Apply u-substitution

: \int - 20000 e^{u} d u

= 100 \cdot \int - 20000 e^{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 100 (- 20000 \cdot \int e^{u} d u)

Use the common integral:

\int e^{u} d u = e^{u}

= 100 (- 20000 e^{u})

Substitute back

u = - \frac{x ^{2}}{40000}

= 100 (- 20000 e^{- \frac{x ^{2}}{40000}})

Simplify

= - 2000000 e^{- \frac{x ^{2}}{40000}}

Add a constant to the solution

= - 2000000 e^{- \frac{x ^{2}}{40000}} + C

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What is the integral of 100e^{-(x/(200))^2}*x ?
The integral of 100e^{-(x/(200))^2}*x is -2000000e^{-(x^2)/(40000)}+C