# Restricted values of x for an indefinite integral?

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• Feb 9th 2011, 01:14 PM
DannyMath
Restricted values of x for an indefinite integral?
Hi all,

I did this problem for my assignment:

integrate: -4cos^2(x)tan^3(x)

I answered:

4ln(abs(cos(x))) - 2cos^2(x) + C

Would this answer be considered correct? Wolfram alpha has one extra step after this answer, something about restricting the x values? Thanks for any clarification.
• Feb 9th 2011, 01:25 PM
CSM
Tan is just sin/cos so your expression becomes (-4sin^3(x)/cos(x))
which integrates to 4 ln(cos(x))-cos(2x)+c
that's all. No restrictions to x. Maybe wolfram gives a plot or something, and of course you cannot plot a graph for x being infinite :p
• Feb 9th 2011, 01:32 PM
DannyMath
Oh I think I understand. The thing is, Wolfram's second last step WAS the answer I posted, and they got from that answer to the one you gave. I was confused about how to go from mine to yours, but I think it's from using the (1/2)(1+cos(2x)) = cos^2(x) identity? Because the 1 ends up being absorbed into the C constant. Is that the step?

This is what wolfram says:

"Which is equivalent for restricted x values to:
= 4 log(cos(x))-cos(2 x)+constant"

where log is the natural log
• Feb 9th 2011, 02:01 PM
Archie Meade
The restriction relates to the fact that x cannot be any odd multiple of $\frac{\pi}{2}$

since the function has $cosx$ in the denominator.

Your answer is equivalent to Wolfram's as only an identity was used.
• Feb 9th 2011, 05:43 PM
topsquark
Quote:

Originally Posted by CSM
Tan is just sin/cos so your expression becomes (-4sin^3(x)/cos(x))
which integrates to 4 ln(cos(x))-cos(2x)+c
that's all. No restrictions to x. Maybe wolfram gives a plot or something, and of course you cannot plot a graph for x being infinite :p

log(cos(x)) does not exist for all x....

-Dan