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Calculus, MET2 2016 VCAA 9 MC

Given that  `(d(xe^(kx)))/(dx) = (kx + 1)e^(kx)`, then  `int xe^(kx) dx` is equal to

  1. `(xe^(kx))/(kx + 1) + c`
  2. `((kx + 1)/k)e^(kx) + c`
  3. `1/k int e^(kx) dx`
  4. `1/k (xe^(kx) - int e^(kx) dx) + c`
  5. `1/k^2 (xe^(kx) - e^(kx)) + c`
Show Answers Only

`D`

Show Worked Solution
♦ Mean mark 41%.
`int (kx + 1)e^(kx) dx` `= xe^(kx) + c_1`
`k int xe^(kx) dx + int e^(kx) dx` `= xe^(kx) + c_1`
`k int xe^(kx) dx` `= xe^(kx) – int e^(kx) dx + c_1`
`:. int xe^(kx) dx` `= 1/k (xe^(kx) – int e^(kx) dx) + c`

 
`=>   D`