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

The integral of e^{u/2} is 2e^{u/2}+C

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integral of e^{u/2}

\int e^{\frac{u}{2}} d u

2 e^{\frac{u}{2}} + C

Solution steps

\int e^{\frac{u}{2}} d u

Apply u-substitution

: \int e^{v} \cdot 2 d v

= \int e^{v} \cdot 2 d v

Take the constant out:

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

= 2 \cdot \int e^{v} d v

Use the common integral:

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

= 2 e^{v}

Substitute back

v = \frac{u}{2}

= 2 e^{\frac{u}{2}}

Add a constant to the solution

= 2 e^{\frac{u}{2}} + C

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