What is the integral of 3e^{0.6x} ?

The integral of 3e^{0.6x} is 5e^{0.6x}+C

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integral of 3e^{0.6x}

\int 3 e^{0.6 x} d x

5 e^{0.6 x} + C

Solution steps

\int 3 e^{0.6 x} d x

Take the constant out:

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

= 3 \cdot \int e^{0.6 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{0.6} d u

= 3 \cdot \int e^{u} \frac{1}{0.6} d u

Take the constant out:

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

= 3 \cdot \frac{1}{0.6} \cdot \int e^{u} d u

Simplify

= 3 \cdot 1.66666 \dots \cdot \int e^{u} d u

Use the common integral:

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

= 3 \cdot 1.66666 \dots e^{u}

Substitute back

u = 0.6 x

= 3 \cdot 1.66666 \dots e^{0.6 x}

Simplify

= 5 e^{0.6 x}

Add a constant to the solution

= 5 e^{0.6 x} + C

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