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

integral

(2 x - 1) e^{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

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

\frac{5 x ^{2}}{( x - 2 ) ( x ^{2} + 1 )}

\frac{( x + 1 )}{( x ^{2} + x - 1 )}

9 cos^{2} (x)

x lo g_{10} (x^{2} + 5)