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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 |
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Answer» `(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` |
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