What is the integral of (e^{bx}*x) ?

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

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integral of (e^{bx}*x)

\int (e^{b x} \cdot x) d x

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

Solution steps

\int e^{b x} x d x

Apply Integration By Parts

= 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

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