Question

Hey guys , about proving integral secx = ln secx+tanx

since ln is an abs value , my prof said that he don't need how to get the answer , he just wants me to take the derivative of secx+tanx , but he also said I should consider it when it's positive and negative ? how can I solve it if it's negative ?

Answer 1

ln(-a) tends to be a complex value, if memory serves

Answer 2

The problem is it's been about 4 years since I've taking calculus that involves complex numbers. :(

Answer 3

i'm not sure about positive and negative , but when I did it I took the derivative of secx+tanx over secx+tanx which will be secx , i'm not sure if this is enough or what :D

Answer 4

\[\int sec(x)\frac{sec(x)+tan(x)}{sec(x)+tan(x)}dx\]
\[\int \frac{sec^2(x)+sec(x)tan(x)}{tan(x)+sec(x)}dx\]
the top is the derivative of the bottom .... which ideally ints up to ln|u|

sec+tan has 0 and negative parts .... so i am not sure what the added +- is spose to suggest

Answer 5

well , I'm confused :D

I remember him saying since it's abs check both negative and positive

I already simplified after taking the derivative of ln abs u and got secx .

Answer 6

it seems that log(-x) = log(x) + i pi

Answer 7

and i represent an imaginary ? but how could I SOLVE IT ?

Answer 8

i pi is just a constant, but then i dont know if this is the right track to take :/

Answer 9

well , I'm kinda confused right now , first I thought he was just trying to explain how antiderivatives work , but when I remembered saying look for the negative and positive I got confused .

Answer 10

ask him to explain himself better :)

Answer 11

well I'm pretty sure he'll just say the same things , look for the negative and positive side.

also I remember when we got an abs we use what's called , sorry I don't remember it's name in english , but it's " -b+or- sqrt(b^2-4ac) and check for the zeros or something to see if it's positive or negative

Answer 12

OK GUYS , let me ask this , if I done integrating for example my result was ..:

\[\ln \left| something \right|\]

how can we determine if it was negative to keep the abs , or positive to remove it and replace it by (something) ?

Answer 13

My experience is that you keep the absolute value if what is inside could be negative. You can drop it if it could never be negative.

Answer 14

Such as you could drop the absolute value for ln(x^2) since it can never be negative.

Answer 15

well , in some cases it could be negative , but I think there's a better way to solve and see if it's negative or positive.

Answer 16

Maybe this link will be helpful
http://www.math.ubc.ca/~feldman/m121/secx.pdf

Answer 17

Since it is absolute value, when the inside is negative, take the absolute value before taking the ln.

Answer 18

Thanks buddy , I'll check with my prof and see if he could explain.

Thanks all of u.