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Integrate the following with respect to ...

Integrate the following with respect to x.
`(i) int(2x + 4)/(x^2 + 4x + 6) dx " " (ii) int (e^x)/(e^x - 1) dx " " (iii) int 1/(x log x) dx`
`(iv) int(sin x + cos x)/(sin x - cos x) dx " " (v) int (cos 2x)/((sin x + cos x)^2) dx`.

Text Solution

Verified by Experts

The correct Answer is:
(i) `log |x^2 + 4x + 6| +c`
(ii) `log |e^x - 1| + c`
(iii) `log(log x) + c`
(iv) `log |sin x - cos x| + c`
(v) `1/2 log |1 + sin 2x|+ c`.
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