Integrate the following:
`int(dx)/(5-13sinx)`
(ii) `int(dx)/(13+3cosx+4sinx)`
(iii) `int(dx)/(a^(2)-b^(2)cos^(2)x)(a^(2)gtb^(2))`
(iv) `int(dx)/(a^(2)-b^(2)cos^(2)x)(a^(2)ltb^(2))`
(v) `int(sin2x+sin4x-sin6x)/(1+cos2x+cos4x+cos6x)dx`

Answer

`(1)/(12)ln|(5tan""(1)/(2)xx-25)/(5tan""(1)/(2)x-1)|+c`
`(1)/(6)tan^(-1)((5tan""(1)/(2)x+2)/(6))+c`
`(1)/(asqrt(a^(2)-b^(2)))tan^(-1)((a)/(sqrt(a^(2)-b^(2)))tanx)+c`
`(1)/(2asqrt(a^(2)-b^(2)))log[(atanx-sqrt(b^(2)-a^(2)))/(atanx+sqrt(b^(2)-a^(2)))]+c`
`(1)/(3)ln|sec3x|-(1)/(2)ln|sec2x|-ln|secx|+c`