Indefinite IntegrationHard

Question

The value of ∫ (x eln sin x - cos x) dx is equal to:

Options

A.x cos x + C
B.sin x - x cos x + C
C.-eln x cos x + C
D.sin x + x cos x + C

Solution

∫(xeln sin x - cos x)dx
= ∫x sin x - ∫cos x dx
= - x cos x + ∫cos x dx - ∫cos x dx
= - elnx cos x + C

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