What is the integral of 3e^{5x} ?

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

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integral of 3e^{5x}

\int 3 e^{5 x} d x

\frac{3}{5} e^{5 x} + C

Solution steps

\int 3 e^{5 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^{5 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{5} d u

= 3 \cdot \int e^{u} \frac{1}{5} d u

Take the constant out:

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

= 3 \cdot \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

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

= 3 \cdot \frac{1}{5} e^{u}

Substitute back

u = 5 x

= 3 \cdot \frac{1}{5} e^{5 x}

Simplify

3 \cdot \frac{1}{5} e^{5 x} : \frac{3}{5} e^{5 x}

= \frac{3}{5} e^{5 x}

Add a constant to the solution

= \frac{3}{5} e^{5 x} + C

n = 1 \sum \infty n^{2} \cdot (0.5)^{n}

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\frac{d y}{d x} = - 8 x y^{2}

\frac{\partial}{\partial x} (2 x^{2} y + 3 x y^{2})

n = 1 \sum \infty (\frac{- 1}{2})^{n}