What is the integral of e^{(x^2-2x)/(100)}(20x-20) ?

The integral of e^{(x^2-2x)/(100)}(20x-20) is 1000e^{1/100 (x^2-2x)}+C

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integral of e^{(x^2-2x)/(100)}(20x-20)

\int e^{\frac{x ^{2} - 2 x}{100}} (20 x - 20) d x

1000 e^{\frac{1}{100} (x^{2} - 2 x)} + C

Solution steps

\int e^{\frac{x ^{2} - 2 x}{100}} (20 x - 20) d x

Apply u-substitution

= \int 10 e^{\frac{u}{100}} d u

Take the constant out:

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

= 10 \cdot \int e^{\frac{u}{100}} d u

Apply u-substitution

= 10 \cdot \int e^{v} \cdot 100 d v

Take the constant out:

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

= 10 \cdot 100 \cdot \int e^{v} d v

Use the common integral:

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

= 10 \cdot 100 e^{v}

Substitute back

= 10 \cdot 100 e^{\frac{x ^{2} - 2 x}{100}}

Simplify

10 \cdot 100 e^{\frac{x ^{2} - 2 x}{100}} : 1000 e^{\frac{1}{100} (x^{2} - 2 x)}

= 1000 e^{\frac{1}{100} (x^{2} - 2 x)}

Add a constant to the solution

= 1000 e^{\frac{1}{100} (x^{2} - 2 x)} + C

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What is the integral of e^{(x^2-2x)/(100)}(20x-20) ?
The integral of e^{(x^2-2x)/(100)}(20x-20) is 1000e^{1/100 (x^2-2x)}+C