Question

∫sin^2x/cos^4x dx

Answer 1

= tan^2 x sec^2x

Answer 2

sin^2 + cos^2 =1

tan^2 + 1 = sec^2

Answer 3

so integrad becomes sec^2(x) [ sec^2 (x) -1 ]

Answer 4

expanding

sec^4(x) -sec^2(x) , now sec^2 integrals to tan

so we look to rewrite the sec^4(x)

Answer 5

Thank you but how can i rewrite sec^4(x)

Answer 6

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

Answer 7

your teacher shouldnt be asking you to do this question

Answer 8

if a software package has trouble doing it then how can they expect a student to do it

Answer 9

This question was in my book the answer is 1/3tan^3(x) but hhats all they've wrote

Answer 10

yeh im so stupid

Answer 11

when you get to tan^2(x)sec^2(x)

you do a substittuion, u= tan(x)

so du= sec^2(x) dx

Answer 12

so you get the integral of u^2 du , which gives the answer

Answer 13

Thank you!