Question

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

Answer 1

what do you need help with?

Answer 2

your substitutions are correct. where did you get stuck?

Answer 3

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

Answer 4

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

Answer 5

From Paul's Online CalcII notes.

Answer 6

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)
\[x/6(e^{6x}) - 1/6 (e^{6x}/6)\]
\[x/6(e^{6x} - 1/36 (e^{6x})\]

Answer 7

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

Answer 8

you're welcome :)