What is the integral of 30e^{0.5x} ?

The integral of 30e^{0.5x} is 60e^{0.5x}+C

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integral of 30e^{0.5x}

\int 30 e^{0.5 x} d x

60 e^{0.5 x} + C

Solution steps

\int 30 e^{0.5 x} d x

Take the constant out:

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

= 30 \cdot \int e^{0.5 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{0.5} d u

= 30 \cdot \int e^{u} \frac{1}{0.5} d u

Take the constant out:

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

= 30 \cdot \frac{1}{0.5} \cdot \int e^{u} d u

Simplify

= 30 \cdot 2 \cdot \int e^{u} d u

Use the common integral:

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

= 30 \cdot 2 e^{u}

Substitute back

u = 0.5 x

= 30 \cdot 2 e^{0.5 x}

Simplify

= 60 e^{0.5 x}

Add a constant to the solution

= 60 e^{0.5 x} + C

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