What is the integral of xe^{bx} ?

The integral of xe^{bx} is e^{bx} 1/b x-e^{bx} 1/(b^2)+C

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integral of xe^{bx}

\int x e^{b x} d x

e^{b x} \frac{1}{b} x - e^{b x} \frac{1}{b ^{2}} + C

Solution steps

\int x e^{b x} d x

Apply Integration By Parts

: e^{b x} \frac{1}{b} x - \int e^{b x} \frac{1}{b} d x

= e^{b x} \frac{1}{b} x - \int e^{b x} \frac{1}{b} d x

\int e^{b x} \frac{1}{b} d x = e^{b x} \frac{1}{b ^{2}}

= e^{b x} \frac{1}{b} x - e^{b x} \frac{1}{b ^{2}}

Add a constant to the solution

= e^{b x} \frac{1}{b} x - e^{b x} \frac{1}{b ^{2}} + C

\int sec^{5} (3 x) d x

\frac{d}{d x} (\frac{2 x y}{( 2 - x ^{2} )})

cos (6 y)

\frac{d}{d x} (\frac{a x + b}{c x + d})

x \to 1 lim (arccos (x))

What is the integral of xe^{bx} ?
The integral of xe^{bx} is e^{bx} 1/b x-e^{bx} 1/(b^2)+C