What is the integral of 9e^{3x} ?

The integral of 9e^{3x} is 3e^{3x}+C

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integral of 9e^{3x}

\int 9 e^{3 x} d x

3 e^{3 x} + C

Solution steps

\int 9 e^{3 x} d x

Take the constant out:

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

= 9 \cdot \int e^{3 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{3} d u

= 9 \cdot \int e^{u} \frac{1}{3} d u

Take the constant out:

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

= 9 \cdot \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= 9 \cdot \frac{1}{3} e^{u}

Substitute back

u = 3 x

= 9 \cdot \frac{1}{3} e^{3 x}

Simplify

9 \cdot \frac{1}{3} e^{3 x} : 3 e^{3 x}

= 3 e^{3 x}

Add a constant to the solution

= 3 e^{3 x} + C

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

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