The integral is given below as, I= #x222B; xsin3x dx Use integration by parts rule. Consider x as first function and sin3x ...

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Integration by Parts

2. x sin 3 x

Question

2. x sin 3x

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Solution

The integral is given below as,

I= ∫ xsin3x dx

Use integration by parts rule. Consider x as first function and sin3xas second function.

I=x ∫ sin3xdx− ∫ ( d dx x ∫ sin3xdx )dx =x( − cos3x 3 )− ∫ ( − cos3x 3 ) dx =− xcos3x 3 + 1 3 ( sin3x 3 )+C I=− xcos3x 3 + 1 9 sin3x+C

Thus, the integration of ∫ xsin3x dx is − xcos3x 3 + 1 9 sin3x+C.

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