a. Integrate this function using integration by parts: x2 sin x dx

x2 sin x dx  image

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2 Answers

Int [x^2 sin(x)] dx

= -x^2 cos(x) - Int[2x (-)cos(x)] dx

= -x^2 cos(x) + 2 (x sin(x) - Int [1sin(X)] dx )

= -x^2 cos(x) + 2 (x sin(x) - [(-)cos (x)]) 

= -x^2 cos(x) + 2x sin(x) + 2 cos (x) +C

= 2x sin(x) + (2-x^2) cos(x) + C

 

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