InterviewSolution
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InterviewSolution
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`int(cosx-1)/(sinx+1).e^(x)dx` is equal toA. `(e^(x)cosx)/(1+sinx)+C`B. `C-(e^(x)sinx)/(1+sinx)`C. `C-(e^(x))/(1+sinx)`D. `C-(e^(x)cosx)/(1+sinx)` |
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Answer» Correct Answer - A Let `l=int(cosx)/(1+sinx).e^(x)dx-int(1)/(sinx+1).e^(x)dx` integration by parts in first integral, we get `((cosx)e^(x))/(1+sinx)-int[(-(1+sinx)sinx-cos^(2)x)/((1+sinx)^(2))].e^(x)dx-int(e^(x))/(sinx+1)dx` `=(e^(x)cosx)/(1+sinx)+int(1)/(1+sinx).e^(x)dx-int(e^(x)dx)/(1+sinx)` `=(e^(x)cosx)/(1+sinx)+C` |
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