The discussion revolves around finding the integral of the function ∫t ln(t + 2) dt. Participants are exploring different approaches to solve this integral, emphasizing the need to use the simplest method as indicated in the problem statement.
The discussion is ongoing, with participants providing feedback on each other's attempts. There is an acknowledgment of potential errors in the integration steps, and some guidance is offered regarding the simplification of expressions. Multiple interpretations of the integral setup are being explored.
Participants are working under the constraint of solving the integral by the simplest method, which may influence their approach and reasoning. There is a focus on ensuring that all steps are clearly articulated and simplified appropriately.
Leave that red part out.chapsticks said:Homework Statement
Find the integral. (Note: Solve by the simplest method - not all require integration by parts.)
∫t ln(t + 2) dt
Homework Equations
∫udv=uv-∫vdu
The Attempt at a Solution
dv=tdt v=tdt=t2/2
u=ln(t+2) du=1/(t+2)dt
Check the vdu in that last integral.∫t ln(t + 2) dt
=(t2/2)ln(t+2)-(1/2)∫(t2/2)dt
chapsticks said:Homework Statement
Find the integral. (Note: Solve by the simplest method - not all require integration by parts.)
∫t ln(t + 2) dt
Homework Equations
∫udv=uv-∫vdu
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?