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

The integral of e^x(2x-2) is 2e^xx-4e^x+C

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integral of e^x(2x-2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

= (2 x - 2) e^{x} - 2 e^{x}

Simplify

(2 x - 2) e^{x} - 2 e^{x} : 2 e^{x} x - 4 e^{x}

= 2 e^{x} x - 4 e^{x}

Add a constant to the solution

= 2 e^{x} x - 4 e^{x} + C

\frac{d}{d x} (\frac{5}{x + 10})

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n = 0 \sum \infty \frac{( 7 - 8 n )}{4 + 3 n}