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

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

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integral of (x-1)e^x

integral

(x - 1) e^{x}

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

f (x) = arctan (x^{\frac{1}{2}})

(x + 2)^{n}

\frac{sin ^{4} ( x )}{cos ( x )}

(cos^{2} (x))^{2}

\frac{1}{( x ^{n} )}