What is the integral of e^{0.3x} ?

The integral of e^{0.3x} is 3.33333…e^{0.3x}+C

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integral of e^{0.3x}

\int e^{0.3 x} d x

3.33333 \dots e^{0.3 x} + C

Solution steps

\int e^{0.3 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{0.3} d u

= \int e^{u} \frac{1}{0.3} d u

Take the constant out:

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

= \frac{1}{0.3} \cdot \int e^{u} d u

Simplify

= 3.33333 \dots \cdot \int e^{u} d u

Use the common integral:

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

= 3.33333 \dots e^{u}

Substitute back

u = 0.3 x

= 3.33333 \dots e^{0.3 x}

Add a constant to the solution

= 3.33333 \dots e^{0.3 x} + C

y^{^{''}} - 2 y^{^{'}} + 50 y = 0, y (0) = \frac{3}{2}, y^{^{'}} (0) = - 9

\int_{0}^{1 - x} 24 y (1 - x - y) d y

4 y^{2}

\int x \cdot sin^{3} (x) d x

y = \frac{6 x}{x + 3}, (- 1, - 3)

What is the integral of e^{0.3x} ?
The integral of e^{0.3x} is 3.33333…e^{0.3x}+C