Question

what is the integral of 5sinh((x/3) - ln(2)) dx?

Answer 1

\[\Large \int\limits 5\sinh\left(\frac{x}{3}-\ln2\right)\; dx\]This?

Answer 2

Do you remember this integral by change?\[\Large \int\limits \sinh x\;dx\]

Answer 3

coshx.. can you show the steps

Answer 4

yes you typed it correctly :)

Answer 5

We have a coefficient of 1/3 attached to our x.
So, the only difference between our integral and the other integral I listed will be that we need to divide by that coefficient when we integrate.

We can do a u-sub if that's too confusing though :)

Answer 6

soo ... sinh(u) dx.... u = ((x/3)-ln(2))... what is the du?

Answer 7

\[\Large 5\int\limits\sinh\left(\color{ #CC0033}{\frac{x}{3}-\ln2}\right)\; dx\]
Letting \(\Large \color{
#CC0033}{u=\dfrac{x}{3}-\ln2}\)
Yah looks good so far :)

Answer 8

and put the 5 in front oftheintegral sign

Answer 9

\[\Large du=\frac{1}{3}\;dx\]Any confusion about that?

Answer 10

what about the ln(2)?

Answer 11

I could show the intermediate step maybe so there's no confusion.\[\Large u=\frac{1}{3}x-\ln2 \qquad\to\qquad \frac{du}{dx}=\frac{1}{3}-0\]

Answer 12

ln(2) is just a constant!! Don't let him confuse you!
He's just a fancy looking constant :D

Answer 13

ok :)... soo its 5 *integral sign* sinh(u) du ...= 5*(1/3)cosh(u)

Answer 14

where do you put the 1/3 in the answer?

Answer 15

Woops one thing to fix real quick.\[\Large du=\frac{1}{3}dx \qquad\to\qquad 3du=dx\]

Answer 16

\[\Large 5\int\limits\limits\sinh\left(\color{ #CC0033}{\frac{x}{3}-\ln2}\right)\; dx \qquad\to\qquad 5\int\limits\limits\sinh\left(\color{ #CC0033}{u}\right)\; (3du)\]

Answer 17

Uh oh, you look confused :3

Answer 18

you bring the 3 in front of the integral sign... I think I get it :)

Answer 19

\[\Large 15\int\limits \sinh u\;du\]Mmm yah that sounds good.

Answer 20

soo= 15cosh((x/3)-ln(2))..?

Answer 21

Yay good job \c:/

Maybe a +C on the end, if you want. But whatever.

Answer 22

ook thanksa ton!!!