16 cos^2 x in terms of sec^2 x

- Im in the middle of solving an integration and just need to know what is

- what is the integral of cosx/sin^2 x
- integral of x^2/(x^2 +1)

thank you

appreciate any help

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- Feb 12th 2009, 07:07 PMalex83just hints in integrals
- Im in the middle of solving an integration and just need to know what is

- what is the integral of cosx/sin^2 x
- integral of x^2/(x^2 +1)

thank you

appreciate any help - Feb 12th 2009, 07:11 PMChop Suey
1. $\displaystyle \sec{x} = \frac{1}{\cos{x}}$

2. You can try $\displaystyle u = \sin{x}$, or maybe it would be more clear if you see it as $\displaystyle \csc{x}\cot{x}$.

3. Simply add 0 using 1. This is a basically a quick way around long division:

$\displaystyle \frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = \ldots$ - Feb 12th 2009, 07:36 PMalex83Chop Suey
Thank you for replying.

the problem is

1- the integral is (sec^2 x +8secx cosx +) so i was trying to find the relation or form of 16cos^2x in terms of the sec^2 x)(Thinking)__16cos^x dx__

2-the integral of this question was (1/(sin^2x) -)**cosx/sin^2x**

3- i got the same result: integral 1+ 1/(x^2+1)

so im looking for the integral of__1/(x^+1)__

THANK YOU AGAIN (Bow) - Apr 24th 2009, 03:32 PMmr fantastic