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`int e^(cotx) (cos x - cosec x ) dx` is equal to : |
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Answer» `int e^(cotx) (cosx-cosecx) dx` Let `y = e^(cotx)sinx` `:. dy/dx = e^cotx cosx +sinx e^cotx(-cosec^2x)` `=> dy/dx = e^cotx cosx - sinx e^cotx(cosec x)` `=> dy/dx = e^cotx(cos-cosecx)` Now, integrating both sides, `y+c = int e^(cotx) (cosx-cosecx) dx` `=> int e^(cotx) (cosx-cosecx) dx = e^(cotx)sinx+c` So, option `D` is the correct option. |
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