using integration by parts evaluate the integral of xsinx between x=0 and x =pi/2

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Why does integration by parts work?


Solve the equation 3sin^2(x) + sin(x) + 8 = 9cos^2(x), -180<X<180. Then find smallest positive solution of 3sin^2(2O-30) + sin(2O-30) + 8 = 9cos^2(2O-30).


How do you integrate sin(3x)cos(5x)?


Find dy/dx when y = x^2(cos(x)).


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