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What is the integral of `1/(cos 2x)?`
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High School Teacher
`int 1/(cos2x) dx`
We know that `secx = 1/(cosx) `
==> `int 1/(cos2x) dx = int sec(2x) dx`
Let `u= 2x ==gt du = 2 dx `
`==gt int sec(2x) dx = int sec(u) (du)/2 = (1/2) int sec(u) du`
Now we know that:
`int sec(u) du = ln (secu + tanu)+ C `
`==gt int 1/(cos2x) dx = (1/2) ln (sec(2x) + tan(2x) )+ C`
Posted by hala718 on May 4, 2012 at 1:41 AM (Answer #1)
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