What is the integral of e^{x/2+3} ?

The integral of e^{x/2+3} is 2e^{x/2+3}+C

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integral of e^{x/2+3}

\int e^{\frac{x}{2} + 3} d x

2 e^{\frac{x}{2} + 3} + C

Solution steps

\int e^{\frac{x}{2} + 3} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= 2 e^{u}

Substitute back

u = \frac{x}{2} + 3

= 2 e^{\frac{x}{2} + 3}

Add a constant to the solution

= 2 e^{\frac{x}{2} + 3} + C

\int \frac{2 y - 1}{y} d y

f (x) = e^{5}

\frac{d}{d x} (- \frac{128 x}{( 16 x ^{2} + 1 ) ^{2}})

f (t) = \frac{2 t}{1 + t ^{2}}

f (x) = 10 x^{4}