求不定积分∫sin^2xcos^5xdx

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求不定积分∫sin^2*xcos^5*xdx求不定积分∫sin^2*xcos^5*xdx求不定积分∫sin^2*xcos^5*xdx∫(sinx)^2(cosx)^5dx=∫(sinx)^2(cosx

求不定积分∫sin^2*xcos^5*xdx
求不定积分∫sin^2*xcos^5*xdx

求不定积分∫sin^2*xcos^5*xdx
∫(sinx)^2(cosx)^5dx
=∫(sinx)^2(cosx)^4d(sinx)
=∫(sinx)^2(1-(sinx)^2)^2d(sinx)
=∫[(sinx)^6-2(sinx)^4+(sinx)^2]d(sinx)
=1/7(sinx)^7-2/5(sinx)^5+1/3(sinx)^3+C

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