What is the integral of e^{x/(12)} ?

The integral of e^{x/(12)} is 12e^{x/(12)}+C

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integral of e^{x/(12)}

\int e^{\frac{x}{12}} d x

12 e^{\frac{x}{12}} + C

Solution steps

\int e^{\frac{x}{12}} d x

Apply u-substitution

: \int e^{u} \cdot 12 d u

= \int e^{u} \cdot 12 d u

Take the constant out:

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

= 12 \cdot \int e^{u} d u

Use the common integral:

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

= 12 e^{u}

Substitute back

u = \frac{x}{12}

= 12 e^{\frac{x}{12}}

Add a constant to the solution

= 12 e^{\frac{x}{12}} + C

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What is the integral of e^{x/(12)} ?
The integral of e^{x/(12)} is 12e^{x/(12)}+C