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Integrate the following functions: (cosx-sinx)/(1+sin(2x) |
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Answer» SOLUTION :`(cosx-sinx)/(1+sin2x) = (cosx-sinx)/(cosx+sinx)^2` `int(cosx-sinx)/(1+sin2x) DX` = `int (cosx-sinx)/9cosx+sinx)^2 dx` LET t = cosx+sinx. Then `dt = (-sinx+cosx)dx` therefore` int(cosx-sinx)/(1+sin2x) dx` =`int dt/t^2 = -1/t+c` = `-1/(cosx+sinx)+c` |
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