What is the integral of (x^2-3x+5)e^x ?

The integral of (x^2-3x+5)e^x is e^xx^2-5e^xx+10e^x+C

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integral of (x^2-3x+5)e^x

\int (x^{2} - 3 x + 5) e^{x} d x

e^{x} x^{2} - 5 e^{x} x + 10 e^{x} + C

Solution steps

\int (x^{2} - 3 x + 5) e^{x} d x

Apply Integration By Parts

: (x^{2} - 3 x + 5) e^{x} - \int (2 x - 3) e^{x} d x

= (x^{2} - 3 x + 5) e^{x} - \int (2 x - 3) e^{x} d x

\int (2 x - 3) e^{x} d x = 2 e^{x} x - 5 e^{x}

= (x^{2} - 3 x + 5) e^{x} - (2 e^{x} x - 5 e^{x})

Simplify

(x^{2} - 3 x + 5) e^{x} - (2 e^{x} x - 5 e^{x}) : e^{x} x^{2} - 5 e^{x} x + 10 e^{x}

= e^{x} x^{2} - 5 e^{x} x + 10 e^{x}

Add a constant to the solution

= e^{x} x^{2} - 5 e^{x} x + 10 e^{x} + C

[x + (x + sin (2) (x))^{7}]^{3}

7 x - x^{2}

f (x) = \frac{3}{4} x + 7

\int - 3 cot (t) d t

\int (\frac{x + 5}{x ^{2} + x - 6}) d x

What is the integral of (x^2-3x+5)e^x ?
The integral of (x^2-3x+5)e^x is e^xx^2-5e^xx+10e^x+C