anonymous
  • anonymous
what is the integral of 5sinh((x/3) - ln(2)) dx?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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zepdrix
  • zepdrix
\[\Large \int\limits 5\sinh\left(\frac{x}{3}-\ln2\right)\; dx\]This?
zepdrix
  • zepdrix
Do you remember this integral by change?\[\Large \int\limits \sinh x\;dx\]
anonymous
  • anonymous
coshx.. can you show the steps

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anonymous
  • anonymous
yes you typed it correctly :)
zepdrix
  • zepdrix
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 :)
anonymous
  • anonymous
soo ... sinh(u) dx.... u = ((x/3)-ln(2))... what is the du?
zepdrix
  • zepdrix
\[\Large 5\int\limits\sinh\left(\color{ #CC0033}{\frac{x}{3}-\ln2}\right)\; dx\] Letting \(\Large \color{ #CC0033}{u=\dfrac{x}{3}-\ln2}\) Yah looks good so far :)
anonymous
  • anonymous
and put the 5 in front oftheintegral sign
zepdrix
  • zepdrix
\[\Large du=\frac{1}{3}\;dx\]Any confusion about that?
anonymous
  • anonymous
what about the ln(2)?
zepdrix
  • zepdrix
I could show the intermediate step maybe so there's no confusion.\[\Large u=\frac{1}{3}x-\ln2 \qquad\to\qquad \frac{du}{dx}=\frac{1}{3}-0\]
zepdrix
  • zepdrix
ln(2) is just a constant!! Don't let him confuse you! He's just a fancy looking constant :D
anonymous
  • anonymous
ok :)... soo its 5 *integral sign* sinh(u) du ...= 5*(1/3)cosh(u)
anonymous
  • anonymous
where do you put the 1/3 in the answer?
zepdrix
  • zepdrix
Woops one thing to fix real quick.\[\Large du=\frac{1}{3}dx \qquad\to\qquad 3du=dx\]
zepdrix
  • zepdrix
\[\Large 5\int\limits\limits\sinh\left(\color{ #CC0033}{\frac{x}{3}-\ln2}\right)\; dx \qquad\to\qquad 5\int\limits\limits\sinh\left(\color{ #CC0033}{u}\right)\; (3du)\]
zepdrix
  • zepdrix
Uh oh, you look confused :3
anonymous
  • anonymous
you bring the 3 in front of the integral sign... I think I get it :)
zepdrix
  • zepdrix
\[\Large 15\int\limits \sinh u\;du\]Mmm yah that sounds good.
anonymous
  • anonymous
soo= 15cosh((x/3)-ln(2))..?
zepdrix
  • zepdrix
Yay good job \c:/ Maybe a +C on the end, if you want. But whatever.
anonymous
  • anonymous
ook thanksa ton!!!

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