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Question
Integrate the function in x sin 3x.
Solution
Let `I = int x. sin 3x dx`
`= x int sin 3x dx - int [d/dx x int sin 3x dx] dx`
`= x (- (cos 3x)/3) - int 1 ((- cos 3x)/3) dx`
`= (x cos 3x)/3 + 1/3 int cos 3x dx`
`= (x cos 3x)/3 + 1/3* (sin 3x)/3 + C`
`= - (x cos 3x)/3 + 1/9 sin 3x + C`
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