Use the identity sin^2(y) + piersonforcongress.coms^2(y) = 1 to obtain the expression sin^2(3x) (1-sin^2(3x)) piersonforcongress.coms(3x) dx.Use the substitution u= sin(3x) by separating the expression through the derivative, u’= 3piersonforcongress.coms(3x).The expression then bepiersonforcongress.commes u^2 (1-u^2) (1/3) du. Now every little thing is in regards to u for this reason we deserve to expand and integrate.Expanding gives (1/3) u^2 - (1/3) u^4 du.The prize in regards to u is currently (1/9) u^3 - (1/15) u^5 + C. Don’t forget the +C!!!Finally, substitute ago into x to get (1/9) sin^3(3x) - (1/15) sin^5(3x) +C.
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