integral of secx!??? Watch

Emily321
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whats the integral of secx!?? is it log mod something? thankyou em xx
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FWoodhouse
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\int \sec x \, \mathrm{d}x = \ln | \sec x + \tan x | + C
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Kolya
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(Original post by FWoodhouse)
\int \sec x \, \mathrm{d}x = \ln | \sec x + \tan x | + C
Francis is always in the zone
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FWoodhouse
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(Original post by Lusus Naturae)
Francis is always in the zone
I know math-fu.
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andy5788
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The above.

If your interested in how to do it it requires a strange method like multiplying by sec squared + tan squared/ sec squared + tan squared or something.

Whatever it is it's not something that would ever occur to you to do if its the one I'm thinking of.
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r3m0t
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As the result results, multiply the integrand by "sec x + tan x" to get int f'(x)/f(x) dx.

Alternatively, use the substitution "tan (t/2)" (find a formula for sec x not involving trigonometric functions).
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generalebriety
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Yeah, everyone's already said it, but I'll repeat in nice maths notation. :p:

\huge \int \sec x \, \text{d} x = \int \frac{\sec x(\sec x + \tan x)}{\sec x + \tan x} \, \text{d} x = \int \frac{\sec  ^2 x + \sec x \tan x}{\sec x + \tan x} \, \text{d} x
\huge = \int \frac{\frac{\text{d}}{\text{d} x} ( \sec x + \tan x )}{\sec x + \tan x} \, \text{d} x = \ln | \sec x + \tan x | + c
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