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

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

Popular >

integral of e^{-2/3 x}

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

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

Solution steps

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Apply u-substitution

: \int - \frac{3}{2} e^{u} d u

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = - \frac{2 x}{3}

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

Add a constant to the solution

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

\int 4 x^{3} - x d x

\int \frac{8 x ^{2} + x}{( 16 x ^{3} + 3 x ^{2} ) ^{2}} d x

\int (4 x^{2} - 3)^{2} d x

\int \frac{2 x ^{4} - 2 x ^{3} + x + 1}{x ^{3} - x ^{2}} d x

What is the integral of e^{-2/3 x} ?
The integral of e^{-2/3 x} is -3/2 e^{-(2x)/3}+C