integrate: sin^3(x)*cos^3(x)dx
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Dec 3, 2007 #2 Re: intergating sin and cos ∫sin3(x)cos3(x)dx\displaystyle \int{sin^{3}(x)cos^{3}(x)}dx∫sin3(x)cos3(x)dx Rewrite: ∫sin3(x)(1−sin2(x))cos(x)dx\displaystyle \int{sin^{3}(x)(1-sin^{2}(x))cos(x)}dx∫sin3(x)(1−sin2(x))cos(x)dx ∫(sin3(x)−sin5(x))cos(x)dx\displaystyle \int{(sin^{3}(x)-sin^{5}(x))cos(x)}dx∫(sin3(x)−sin5(x))cos(x)dx Now, let u=sin(x), du=cos(x)dx\displaystyle u=sin(x), \;\ du=cos(x)dxu=sin(x), du=cos(x)dx make the substitutions and integrate.
Re: intergating sin and cos ∫sin3(x)cos3(x)dx\displaystyle \int{sin^{3}(x)cos^{3}(x)}dx∫sin3(x)cos3(x)dx Rewrite: ∫sin3(x)(1−sin2(x))cos(x)dx\displaystyle \int{sin^{3}(x)(1-sin^{2}(x))cos(x)}dx∫sin3(x)(1−sin2(x))cos(x)dx ∫(sin3(x)−sin5(x))cos(x)dx\displaystyle \int{(sin^{3}(x)-sin^{5}(x))cos(x)}dx∫(sin3(x)−sin5(x))cos(x)dx Now, let u=sin(x), du=cos(x)dx\displaystyle u=sin(x), \;\ du=cos(x)dxu=sin(x), du=cos(x)dx make the substitutions and integrate.
