What is the integral of ((3x)/2-9/4)e^{x(x-3)} ?

The integral of ((3x)/2-9/4)e^{x(x-3)} is 3/4 e^{x(x-3)}+C

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integral of ((3x)/2-9/4)e^{x(x-3)}

\int (\frac{3 x}{2} - \frac{9}{4}) e^{x (x - 3)} d x

\frac{3}{4} e^{x (x - 3)} + C

Solution steps

\int (\frac{3 x}{2} - \frac{9}{4}) e^{x (x - 3)} d x

Apply u-substitution

= \int \frac{3 e ^{u}}{4} d u

Take the constant out:

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

= \frac{3}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{3}{4} e^{u}

Substitute back

u = x (x - 3)

= \frac{3}{4} e^{x (x - 3)}

Add a constant to the solution

= \frac{3}{4} e^{x (x - 3)} + C

What is the integral of ((3x)/2-9/4)e^{x(x-3)} ?
The integral of ((3x)/2-9/4)e^{x(x-3)} is 3/4 e^{x(x-3)}+C