What is the integral of (4x-7)e^x ?

The integral of (4x-7)e^x is 4e^xx-11e^x+C

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integral of (4x-7)e^x

\int (4 x - 7) e^{x} d x

4 e^{x} x - 11 e^{x} + C

Solution steps

\int (4 x - 7) e^{x} d x

Apply Integration By Parts

: (4 x - 7) e^{x} - \int 4 e^{x} d x

= (4 x - 7) e^{x} - \int 4 e^{x} d x

\int 4 e^{x} d x = 4 e^{x}

= (4 x - 7) e^{x} - 4 e^{x}

Simplify

(4 x - 7) e^{x} - 4 e^{x} : 4 e^{x} x - 11 e^{x}

= 4 e^{x} x - 11 e^{x}

Add a constant to the solution

= 4 e^{x} x - 11 e^{x} + C

\int_{0}^{6} 1 + x^{4} + 2 x^{2} d x

\frac{d}{d y} (\frac{A}{[ - 4.2 ]} y \frac{B}{( - 1.5 )})

k = 1 \sum \infty k e^{- k^{2}}

\frac{1}{2} (1 + cos (2 x))

x \to - 1 lim (2 e^{x - 1})