What is the integral of (2x-1)e^x ?

The integral of (2x-1)e^x is 2e^xx-3e^x+C

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integral of (2x-1)e^x

\int (2 x - 1) e^{x} d x

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

Solution steps

\int (2 x - 1) e^{x} d x

Apply Integration By Parts

: (2 x - 1) e^{x} - \int 2 e^{x} d x

= (2 x - 1) e^{x} - \int 2 e^{x} d x

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

= (2 x - 1) e^{x} - 2 e^{x}

Simplify

(2 x - 1) e^{x} - 2 e^{x} : 2 e^{x} x - 3 e^{x}

= 2 e^{x} x - 3 e^{x}

Add a constant to the solution

= 2 e^{x} x - 3 e^{x} + C

f (x) = x^{2} - 2 x + 3

f (x) = 9 x - 6 x, at x = 1

\frac{d}{d x} ((x)^{4})

\int \frac{sec ^{2} ( \frac{1}{x ^{3}} )}{x ^{4}} d x