Integral of \( \displaystyle 3 x e^{- 3 x} \)

Problem 4.731 · medium

1. \[ \int 3 x e^{- 3 x}\, dx \]
   integral algebraStart with the integral of the given function. Rearrange the integrand to prepare for integration by parts.✓ Proved
2. \[ = - x e^{- 3 x} - \int \left(- e^{- 3 x}\right)\, dx \]
   partsApply integration by parts with u = x and dv = 3*exp(-3*x) dx.✓ Proved
3. \[ = - x e^{- 3 x} + \int e^{- 3 x}\, dx \]
   algebraDistribute the negative sign and simplify the integral term.✓ Proved
4. \[ = - x e^{- 3 x} - \frac{e^{- 3 x}}{3} \]
   antiderivativeEvaluate the remaining integral.✓ Proved