What is the integral of (3x-11)e^x ?

The integral of (3x-11)e^x is 3e^xx-14e^x+C

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integral of (3x-11)e^x

\int (3 x - 11) e^{x} d x

3 e^{x} x - 14 e^{x} + C

Solution steps

\int (3 x - 11) e^{x} d x

Apply Integration By Parts

: (3 x - 11) e^{x} - \int 3 e^{x} d x

= (3 x - 11) e^{x} - \int 3 e^{x} d x

\int 3 e^{x} d x = 3 e^{x}

= (3 x - 11) e^{x} - 3 e^{x}

Simplify

(3 x - 11) e^{x} - 3 e^{x} : 3 e^{x} x - 14 e^{x}

= 3 e^{x} x - 14 e^{x}

Add a constant to the solution

= 3 e^{x} x - 14 e^{x} + C

3 y^{^{''}} - 7 y^{^{'}} + 2 y = 0, y (0) = - 3, y^{^{'}} (0) = - 8

\int sin (x) - 8 cos (x) d x

f (x) = cot (7 x)

x \to 0 lim \frac{( \frac{1}{( x + 4 )} ) - ( \frac{1}{4} )}{x}

5 x + 8

What is the integral of (3x-11)e^x ?
The integral of (3x-11)e^x is 3e^xx-14e^x+C