What is the integral of 10e^{x/(20)} ?

The integral of 10e^{x/(20)} is 200e^{x/(20)}+C

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integral of 10e^{x/(20)}

\int 10 e^{\frac{x}{20}} d x

200 e^{\frac{x}{20}} + C

Solution steps

\int 10 e^{\frac{x}{20}} d x

Take the constant out:

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

= 10 \cdot \int e^{\frac{x}{20}} d x

Apply u-substitution

= 10 \cdot \int e^{u} \cdot 20 d u

Take the constant out:

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

= 10 \cdot 20 \cdot \int e^{u} d u

Use the common integral:

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

= 10 \cdot 20 e^{u}

Substitute back

u = \frac{x}{20}

= 10 \cdot 20 e^{\frac{x}{20}}

Simplify

= 200 e^{\frac{x}{20}}

Add a constant to the solution

= 200 e^{\frac{x}{20}} + C

What is the integral of 10e^{x/(20)} ?
The integral of 10e^{x/(20)} is 200e^{x/(20)}+C