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Help with a trig integration

  • Thread starter mk200789
  • Start date
  • #1
7
0

Homework Statement


integrate tan(x)sec^4(x) dx


Homework Equations





The Attempt at a Solution


int tan(x)sec^4(x) dx
= int tan(x)sec^2(x)sec^2(x) dx
= int tan(x)sec^2(x) (tan^2(x)+1) dx

let u = tanx ==> du = sec^2(x) dx

= int usec^2(x) (u^2 + 1) /sec^2(x) du
= int u(u^2+1) du
= u^4/4 + u^2/2 + C
and then replace the u with tanx

am i doing this correct?
 

Answers and Replies

  • #2
Char. Limit
Gold Member
1,204
12
Absolutely. If you want, you can unfactor the answer, but it isn't necessary.
 
  • #3
7
0
ttthank you!
 

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