Question

Integrate (e^8x)cos7x

Answer 1

This is by parts integration

Answer 2

I have so far

\[\frac{ \cos7x*e^8x) }{ 8 }+7/8[\frac{ \sin7xe^8x }{ 8 }-7/8\int\limits_{}^{}\cos7xe^8xdx\]

Answer 3

Basically the integral repeats itself and I do not know how to solve for it. I know I am supposed to set the repeteing part to a varible, Q, and then solve for it

Answer 4

Use the draw feature to write the integral you want us to solve

Answer 5

when the integral repeats you can just transpose it to the other side. For better understanding let me give an example (note: this is not a correct integration. i'm just showing how the transposing works)
\[\int 2xdx = 1 - \int 2xdx\]
\[\int 2xdx + \int 2xdx = 1\]
\[2\int 2xdx = 1\]
\]\int 2xdx = \frac 12\]
get the idea?

Answer 6

that last part is \[\int 2xdx = \frac 12\] latex fail

Answer 7

Let me draw and see if I understand the transpose

Answer 8

sure

Answer 9

remember that your repeated integral is within a quantity multiplied to 7/8 so you have to multiply by 7/8 before transposing

Answer 10

Here's what you have, just written more clearly:
\[\color{red}{\int e^{8x}\cos7x~dx}=\frac{1}{8} \cos7x~e^{8x}+\frac{7}{64}\sin7x~e^{8x}-\frac{7}{8}\color{red}{\int\cos7xe^{8x}~dx}\]
Notice the common terms?

I haven't checked your work, but assuming it's correct so far, this is how you'd proceed.

Answer 11

i think \[\frac 78 \int \cos (7x) e^{8x}dx\] is within the quantity that is multiplied to 7/8 since there was no closing bracket

Answer 12

/I did forget to close bracket. Sorry about that

Answer 13

\[\frac{ 7 }{ 8 }*−7/8∫\cos7xe8x dx\]

Answer 14

yes. that is the value that you transpose

Answer 15

anyway i have to go. if you have any further questions, @SithsAndGiggles will most likely answer