Use the identification sin^2(y) + altoalsimce.orgs^2(y) = 1 to get the expression sin^2(3x) (1-sin^2(3x)) altoalsimce.orgs(3x) dx.Use the substitution u= sin(3x) by separating the expression by the derivative, u’= 3altoalsimce.orgs(3x).The expression climate bealtoalsimce.orgmes u^2 (1-u^2) (1/3) du. Now whatever is in regards to u therefore we can expand and also integrate.Expanding gives (1/3) u^2 - (1/3) u^4 du.The price in regards to u is currently (1/9) u^3 - (1/15) u^5 + C. Don’t forget the +C!!!Finally, substitute back into x to get (1/9) sin^3(3x) - (1/15) sin^5(3x) +C.
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