Lucy
  • Lucy
∫sin^2x/cos^4x dx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
= tan^2 x sec^2x
anonymous
  • anonymous
sin^2 + cos^2 =1 tan^2 + 1 = sec^2
anonymous
  • anonymous
so integrad becomes sec^2(x) [ sec^2 (x) -1 ]

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anonymous
  • anonymous
expanding sec^4(x) -sec^2(x) , now sec^2 integrals to tan so we look to rewrite the sec^4(x)
Lucy
  • Lucy
Thank you but how can i rewrite sec^4(x)
anonymous
  • anonymous
yeh , by checking with wolframa "http://www.wolframalpha.com/input/?i=xtan%28x%29" there is no way to do this with only elementary functions
anonymous
  • anonymous
your teacher shouldnt be asking you to do this question
anonymous
  • anonymous
if a software package has trouble doing it then how can they expect a student to do it
Lucy
  • Lucy
This question was in my book the answer is 1/3tan^3(x) but hhats all they've wrote
anonymous
  • anonymous
yeh im so stupid
anonymous
  • anonymous
when you get to tan^2(x)sec^2(x) you do a substittuion, u= tan(x) so du= sec^2(x) dx
anonymous
  • anonymous
so you get the integral of u^2 du , which gives the answer
Lucy
  • Lucy
Thank you!

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