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

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

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integral of e^{-2x+3}

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

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

Solution steps

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

Apply u-substitution

: \int - \frac{1}{2} e^{u} d u

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = - 2 x + 3

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

Add a constant to the solution

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

x^{2} e^{2 x}

\frac{7}{4} x^{2} - 3 x + 12

4 + 7 x

sin (θ)

\int sin (2 x) sin (3 x) d x

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