Maharashtra State BoardHSC Arts 12th Board Exam
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Evaluate `Integration E^X [(Cosx - Sin X)/Sin^2 X]Dx` - Mathematics and Statistics

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Evaluate `int e^x [(cosx - sin x)/sin^2 x]dx`

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Solution

`I = inte^x [cosx/sin^2x - sinx/sin^2x]dx`

`= int e^x[(cotx.cosecx, -cosecx),(f'(x), f(x))]`

∵ `int e^x[f(x) + f'(x)]dx  = e^x f(x) + C`

`:. I = -e^x.cosec x + C`

Concept: Properties of Definite Integrals
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