Question

indefinite integral help

Not sure how to tackle this question and need some guidance..

Answer 1

did u try substituting \(u = e^{-8x}\)

?

Answer 2

nope, I'm a bit lost sorry. How do you even anti-differentiate 7usin(u)? would it just be \[-\frac{ 7 }{ 2 }u^2\cos(u) + C\] or something similar?

Answer 3

oh so you're not yet been taught the product 'uv' rule for anti-derivative ??

Answer 4

this is more the chain rule i believe ...

Answer 5

u' sin(u) comes from -cos(u)

Answer 6

oh and by the way, you won't get u sin u right?
isn't it just sin u, after substitution?

Answer 7

with a constant

Answer 8

ok, well can you tell me how to do it?

Answer 9

ganesh already did

let u = .... what is du?

Answer 10

or are you talking about the by parts method?

Answer 11

by parts not at all required here...
first find du
and everything will be clear to u

Answer 12

does the e^(-8x) inside the sin only become u?

Answer 13

requesting one more time :
u = e^(-8x)
du =.... ?

Answer 14

you are going to be substituting pieces of the equation:

start with u = e^(-8x) and take the derivative to find out how to replace dx

Answer 15

you can find du, right ?
or du/dx

Answer 16

du/dx = -8e-8x?

Answer 17

-8e^(-8x)

Answer 18

yes!

so,
\(\large e^{(-8x)}dx = (-1/8)du\)
got this ?

this term is present in your integral function!