I'm not sure how to integrate this function. I tried converting the numerator into a(sinx+cosx)+b(cosx-sinx), but I couldn't find anything that worked. It didn't really simplify the integrand.

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- Mar 2nd 2013, 09:38 PMquanta123Integrate (sinx-5cosx)/(sinx+cosx)
I'm not sure how to integrate this function. I tried converting the numerator into a(sinx+cosx)+b(cosx-sinx), but I couldn't find anything that worked. It didn't really simplify the integrand.

- Mar 2nd 2013, 10:36 PMSorobanRe: Integrate (sinx-5cosx)/(sinx+cosx)
Hello, quanta123!

I found a way, but it's pretty elaborate.

I'm sure there is a simpler way.

I used these identities:

. . . . .

. . . . .

n

Quote:

Multiply by

. .

. .

. .

. .

. .

Got it?

- Mar 3rd 2013, 03:40 AMibduttRe: Integrate (sinx-5cosx)/(sinx+cosx)
- Mar 3rd 2013, 06:29 AMEstebanRe: Integrate (sinx-5cosx)/(sinx+cosx)
I think there's a simplest way...

and for the last one integral, using will be using simple algebra with a rectangle triangle with sides - Oct 2nd 2017, 08:21 AMcocoboyRe: Integrate (sinx-5cosx)/(sinx+cosx)
Hello could you elaborate on how you went from your second step to the third one please. And thank you

- Oct 2nd 2017, 08:29 AMSlipEternalRe: Integrate (sinx-5cosx)/(sinx+cosx)
- Oct 4th 2017, 01:52 AMcocoboyRe: Integrate (sinx-5cosx)/(sinx+cosx)