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Question
Evaluate:
`int x^2 cos x dx`
Solution
Let I = `int x^2 cos x dx`
On applying integration by parts
I = `x^2 int cos x dx - int{d/dx (x^2) int cosx.dx}dx`
I = `x^2 sinx - int 2x sinx dx`
Again on applying integration by parts
= x2 sin x – 2[– x cos x – ∫ – cos x dx]
= x2 sin x – 2[– x cos x + sin x + c]
= x2 sin x + 2x cos x – 2 sin x + c
= (x2 – 2) sin x + 2x cos x + c
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