# Find the integral. (Note: Solve by the simplest method )

1. Feb 14, 2012

### chapsticks

1. The problem statement, all variables and given/known data

Find the integral. (Note: Solve by the simplest method - not all require integration by parts.)
∫t ln(t + 2) dt

2. Relevant equations

∫udv=uv-∫vdu

3. The attempt at a solution

dv=tdt v=tdt=t2/2
u=ln(t+2) du=1/(t+2)dt

∫t ln(t + 2) dt
=(t2/2)ln(t+2)-(1/2)∫(t2/2)dt
=(t2/2)ln(t+2)-(1/2)∫(t-2+(4/(t+2))dt
=(t2/2)ln(t+2)-(1/2)[(t2/2)-2t+4ln(t+2)]+C
=? Idk why I keep getting it wrong?

2. Feb 14, 2012

### LCKurtz

Leave that red part out.
Check the vdu in that last integral.

3. Feb 14, 2012

### SammyS

Staff Emeritus
The above line should be:
$\displaystyle (t^2/2)\ln(t+2)-(1/2)\int \frac{t^2}{t+2}\,dt\,.$​

4. Feb 14, 2012

### xaos

it reads okay to me, although you missed a step. are you not simplifying enough?