anonymous
  • anonymous
solve integral (1-tan^2(x))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\int\limits_{?}^{?}1-\tan ^{2}x=\int\limits_{?}^{?}1-(\sec ^{2}x-1)\]
yuki
  • yuki
1-tan^2(x) is a nice Identity... do you know what it is ?
anonymous
  • anonymous
\[=\int\limits_{?}^{?}2-\sec ^{2}x\]

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anonymous
  • anonymous
2x-tanx+C
yuki
  • yuki
just to let you know uzma, if you eliminate the _{}-{} part after "int" the limits of the integral will go away like this \[\int\limits\]
anonymous
  • anonymous
oh thanks, i dint try it :)
yuki
  • yuki
np :)
anonymous
  • anonymous
\[\int\limits\]
yuki
  • yuki
Lao, to remember the integrals of trig, you need to know the derivatives of them very well
anonymous
  • anonymous
right ?:)
yuki
  • yuki
for this one, d/dx(tan(x)) = sec^2(x) was the one tat uzma referred to
yuki
  • yuki
@ uzma fantastic !
anonymous
  • anonymous
thanks
yuki
  • yuki
another one you will see a lot is things like \[\int\limits -\csc(x)\cot(x) dx\]
yuki
  • yuki
if you try to do u-substitution or integration by parts, it will be a tough one, but if you remember d/dx csc(x) = -csc(x)cot(x) then we know that the integral that I showed you will have an ans csc(x) + C

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