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integral of secx!???

whats the integral of secx!?? is it log mod something? thankyou em xx

\int \sec x \, \mathrm{d}x = \ln | \sec x + \tan x | + C

FWoodhouse

\int \sec x \, \mathrm{d}x = \ln | \sec x + \tan x | + C

Francis is always in the zone :biggrin:

:biggrin:

Lusus Naturae

Francis is always in the zone :biggrin:

:biggrin:

I know math-fu.

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.

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).

Yeah, everyone's already said it, but I'll repeat in nice maths notation. :p:

: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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