What is the integral of 5e^{0.3x} ?

The integral of 5e^{0.3x} is 16.66666…e^{0.3x}+C

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integral of 5e^{0.3x}

\int 5 e^{0.3 x} d x

16.66666 \dots e^{0.3 x} + C

Solution steps

\int 5 e^{0.3 x} d x

Take the constant out:

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

= 5 \cdot \int e^{0.3 x} d x

Apply u-substitution

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

= 5 \cdot \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

= 5 \cdot \frac{1}{0.3} \cdot \int e^{u} d u

Simplify

= 5 \cdot 3.33333 \dots \cdot \int e^{u} d u

Use the common integral:

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

= 5 \cdot 3.33333 \dots e^{u}

Substitute back

u = 0.3 x

= 5 \cdot 3.33333 \dots e^{0.3 x}

Simplify

= 16.66666 \dots e^{0.3 x}

Add a constant to the solution

= 16.66666 \dots e^{0.3 x} + C

\frac{\partial}{\partial x} (\frac{x}{t})

\frac{d}{d x} (tan (5 x^{3}))

\int e^{2 x} ln (e^{x}) d x

y = x^{2} - 8 x, at x = - 8

\frac{d}{d y} (e^{x y z})

What is the integral of 5e^{0.3x} ?
The integral of 5e^{0.3x} is 16.66666…e^{0.3x}+C