Integration by Parts

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



Evaluate the integral. (Use C for the constant of integration.)



∫te ^ (-9t) dt





2. Relevant equations



∫udv = uv - ∫vdu



u=t dv= (-1/9) e ^(-9t)

du=dt v=e ^ (-9t) dt



3. The attempt at a solution



= -1/9 te^(-9t) - ∫-1/9 e ^(-9t) dt



Second Integral:

w=-9t

dw=-9dt

-81∫-1/9 * -81 e ^(-9t) dt

-81∫e^w * w

-81 * e^(-9t) +C



Final Answer:

= -1/9 te^(-9t) + 81 e ^(-9t) +C



This answer isn't right and I'm not sure where I'm going wrong, so any help would be appreciated. Thanks!!