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

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

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integral of e^{-3/2 x}

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

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

Solution steps

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

Multiply fractions:

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

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

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

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

Add a constant to the solution

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

6 x^{3} - 9 x^{2} + 5 x - 2

7 cos (π x), 8 x^{2} - 2, [- 0.5, 0.5]

x \to - 1 lim (\frac{3 x ^{2} - 9 x - 12}{3 x + 3})

\int \frac{6 + x}{36 - x ^{2}} d x

\frac{d y}{d x}, 7 x y + 1 = 0

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