What is the integral of (-3x+2)e-x ?

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

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integral of (-3x+2)e-x

\int (- 3 x + 2) e - x d x

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

Solution steps

\int (- 3 x + 2) e - x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int (- 3 x + 2) e d x - \int x d x

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

\int x d x = \frac{x ^{2}}{2}

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

Add a constant to the solution

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

x \to 3 lim (\frac{( x ^{2 - 7 x + 12} )}{( 3 - x )})

\int \frac{y}{( y + 1 ) ^{2}} d y

x \to \infty lim (- 2 x e^{- 2 x})

y = \frac{1}{2 cos ^{2} ( x )}

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