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

The integral of-e^{3x} is -1/3 e^{3x}+C

Popular >

integral of-e^{3x}

\int - e^{3 x} d x

- \frac{1}{3} e^{3 x} + C

Solution steps

\int - e^{3 x} d x

Take the constant out:

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

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

Apply u-substitution

: \int e^{u} \frac{1}{3} d u

= - \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

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

Use the common integral:

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

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

Substitute back

u = 3 x

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

Add a constant to the solution

= - \frac{1}{3} e^{3 x} + C

\frac{2 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

\int \frac{y}{x z} d x

\frac{s + 2}{( s - 2 ) ( s + 1 )}

\int 2 x y - sin (x) d x

f (x) = (x + 1) (3 x^{2} - 5 x + 2)