What is the integral of-2e^{3x} ?

The integral of-2e^{3x} is -2/3 e^{3x}+C

integral of-2e^{3x}

\int - 2 e^{3 x} d x

- \frac{2}{3} e^{3 x} + C

Solution steps

\int - 2 e^{3 x} d x

Take the constant out:

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

= - 2 \cdot \int e^{3 x} d x

Apply u-substitution

= - 2 \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

= - 2 \cdot \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= - 2 \cdot \frac{1}{3} e^{u}

Substitute back

u = 3 x

= - 2 \cdot \frac{1}{3} e^{3 x}

Simplify

- 2 \cdot \frac{1}{3} e^{3 x} : - \frac{2}{3} e^{3 x}

= - \frac{2}{3} e^{3 x}

Add a constant to the solution

= - \frac{2}{3} e^{3 x} + C

\int \frac{3}{2} ln x^{3} + 1 d x

d er i v a t i v e f (x) = \frac{x}{x - 1}

t an g e n t f (x) = 3 - 5 x + 2 x^{2}, (- 9, 210)

(x + y)^{2} d x + (2 x y + x^{2} - 9) d y = 0

x \to \infty lim (\frac{x}{2 x})