Posted by chris on Sunday, February 27, 2011 at 2:15pm.
|x^2*cos^2(x) dx =
=|x^2*(1/2)(1+cos(2x)) dx
=(1/2)|x^2 dx + (1/2)|x^2*cos(2x) dx
=(1/6)x^3 + (1/2)|x^2*cos(2x) dx
Using integration by part:
u = x^2
du = 2x dx
dv = cos(2x) dx
v = (1/2) sin(2x)
|x^2*cos(2x) dx =
= (1/2)x^2*sin(2x) - |xsin(2x) dx
Again, using integration by part:
u = x
du = dx
dv = sin(2x) dx
v = -(1/2)cos(2x)
|x^2*cos(2x) dx =
= (1/2)x^2*sin(2x) - {-(1/2)x*cos(2x) + (1/2)|cos(2x) dx}
= (1/2)x^2*sin(2x) + (x/2)cos(2x) - (1/4)sin(2x) + const
Finally, we have:
|x^2*cos^2(x) dx =
= (1/6)x^3 + (1/4)x^2*sin(2x) + (x/4)cos(2x) - (1/8)sin(2x) + const
Related Questions
math - use integration by parts to prove the following reduction formula: |cos^...
Integral calculus - Please can anyone help with the following problems - thanks...
Integration - 1. [integration] (3x+7sin(x))^2 dx i tried 3 different methods of ...
possible functions - How to find all possible functions of f with a given ...
calculus - reverse the order of integration integration 1-e integration 0-lnx ...
Integration? - Sorry, i have a load of questions on integration... thanks for ...
Integration - Intergrate ¡ì sec^3(x) dx could anybody please check ...
Integral - That's the same as the integral of sin^2 x dx. Use integration by...
Calc - evaluate the indefinite integral: x^13(cos(x^7))dx I've tried using ...
Math Integration - i keep getting stuck and i think im missing something ...
For Further Reading
