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Integrals help

Hi,

Am i correct in saying:
integral -(tan(x)) ---> ln(sec(x))

But how come in the back of my book it says:
integral -(tan(x)) ---> ln(cos(x))

Am i missing something?

Thanks
Reply 1
Avatar for ibysaiyan
ibysaiyan
16
You know that tan: sinx/cosx
Still dont get it?
Do substitution let u=cosx. => du/dx=-sinx. So tanx becomes : sinx/cos gets replaced by -du/u. of which the integral is -lnu.
:wink:
matt2minger
Hi,

Am i correct in saying:
integral -(tan(x)) ---> ln(sec(x))





No, this is not correct.
I think you mean integral (tan(x)) ---> ln(sec(x))

matt2minger

But how come in the back of my book it says:
integral -(tan(x)) ---> ln(cos(x))



Which is equivalent to what I wrote above.
Reply 3
Avatar for Pheylan
Pheylan
∫tanx dx=lnsecx+C⇒−∫tanx dx=−lnsecx+C=ln(1secx)+C=lncosx+C\int tanx\ dx=lnsecx+C\Rightarrow-\int tanx\ dx=-lnsecx+C=ln(\frac{1}{secx})+C=lncosx+C

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