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# integral of secx

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1. ....obviously ( I was told this was the first step)

2. (Original post by wcp100)

....obviously ( I was told this was the first step)

Immediately there's a problem as your limits do not make sense. They must either be in radians or as a fraction of 360.

What you need to note is that your integrand can be rewritten as:

What is the derivative of ? Does it look familiar? What do you do with integrals with integrands of the form ? *cough* natural logarithm *cough*.
3. Recall the integral of f'(x)/f(x).
4. I don't like that way of finding the integral of the secant.
It assumes that we already know the answer, doesn't it?
Why the hell would we multiply by that otherwise?
5. this needs to be moved to the health and relationships forum.
6. (Original post by a²+b² = c²)
I don't like that way of finding the integral of the secant.
It assumes that we already know the answer, doesn't it?
Why the hell would we multiply by that otherwise?
You were thinking exactly what I was. Is there another way of doing it ?
7. (Original post by a²+b² = c²)
I don't like that way of finding the integral of the secant.
It assumes that we already know the answer, doesn't it?
Why the hell would we multiply by that otherwise?
(Original post by wcp100)
You were thinking exactly what I was. Is there another way of doing it ?
Yes, there is.

Note that .

Then use a substitution of and use partial fractions.
8. (Original post by wcp100)

....obviously ( I was told this was the first step)

well you could just substitute in du for
and u for

to get

9. (Original post by wcp100)
You were thinking exactly what I was. Is there another way of doing it ?

You can also use the well known t substitution.

t=tan(x/2)

cos x = (1-t^2)/(1+t^2)

dx/dt=2/(1+t^2)

It's all very straightforward and requires no cleverness at all.

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