What is the integral of 0.09e^{0.04x} ?

The integral of 0.09e^{0.04x} is 2.25e^{0.04x}+C

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integral of 0.09e^{0.04x}

\int 0.09 e^{0.04 x} d x

2.25 e^{0.04 x} + C

Solution steps

\int 0.09 e^{0.04 x} d x

Take the constant out:

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

= 0.09 \cdot \int e^{0.04 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{0.04} d u

= 0.09 \cdot \int e^{u} \frac{1}{0.04} d u

Take the constant out:

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

= 0.09 \cdot \frac{1}{0.04} \cdot \int e^{u} d u

Simplify

= 0.09 \cdot 25 \cdot \int e^{u} d u

Use the common integral:

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

= 0.09 \cdot 25 e^{u}

Substitute back

u = 0.04 x

= 0.09 \cdot 25 e^{0.04 x}

Simplify

= 2.25 e^{0.04 x}

Add a constant to the solution

= 2.25 e^{0.04 x} + C

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What is the integral of 0.09e^{0.04x} ?
The integral of 0.09e^{0.04x} is 2.25e^{0.04x}+C