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

The integral of e^{-3x+2} is -1/3 e^{-3x+2}+C

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integral of e^{-3x+2}

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

- \frac{1}{3} e^{- 3 x + 2} + C

Solution steps

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

Apply u-substitution

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

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

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

Add a constant to the solution

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

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

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

f (u) = u

\frac{d}{d x} (\frac{25 - x ^{2}}{8 x})

What is the integral of e^{-3x+2} ?
The integral of e^{-3x+2} is -1/3 e^{-3x+2}+C