ind_int xe^6x dx
u=x
du=dx
dv=e^6x dx
v=(1/6)e^6x

Question

ind_int xe^6x dx
u=x
du=dx 
dv=e^6x dx
v=(1/6)e^6x

anonymous · Answer

what do you need help with?

anonymous · Answer

your substitutions are correct. where did you get stuck?

anonymous · Answer

$$the final ans is (x/6)e ^{6x}-(1/36)e ^{6x}+c....don't get the (1/36) part?? how is \int\limits_{}^{}(1/6)e ^{6x}=(1/36)?$$

anonymous · Answer

$$\int\limits_{}^{}(1/6)e ^{6x}=(1/36)e ^{6x}?$$

anonymous · Answer

From Paul's Online CalcII notes.

anonymous · Answer

i'll just solve it step by step..
$$uv - \int vdu$$
$$x/6 (e^{6x}) - \int 1/6 (e^{6x})dx$$
$$x/6(e^{6x}) - 1/6 \int e^{6x}dx$$
the integral of e^(6x)dx is 1/6 e^(6x) 
$$x/6(e^{6x}) - 1/6 (e^{6x}/6)$$
$$x/6(e^{6x} - 1/36 (e^{6x})$$

anonymous · Answer

It's the obvious points that elude me. Exactly why I'm not so great at math. THanks for your help!

anonymous · Answer

you're welcome :)