2010-04-07, 07:48 PM
u = sin x
du = cos x dx
sin^3(x)cos^5(x)dx = u^3*(1-u^2)^2 du = u^3 - 2u^5 + u^7 du -> 1/4 u^4 - 2/6 u^6 + 1/8 u^8 + C
sin^4(x)cos^5(x)dx = u^4*(1-u^2)^2 du = u^4 - 2u^6 + u^8 du -> 1/5 u^5 - 2/7 u^7 + 1/9 u^9 + C
etc
du = cos x dx
sin^3(x)cos^5(x)dx = u^3*(1-u^2)^2 du = u^3 - 2u^5 + u^7 du -> 1/4 u^4 - 2/6 u^6 + 1/8 u^8 + C
sin^4(x)cos^5(x)dx = u^4*(1-u^2)^2 du = u^4 - 2u^6 + u^8 du -> 1/5 u^5 - 2/7 u^7 + 1/9 u^9 + C
etc