求不定积分∫sin^2xcos^5xdx

来源：学生作业帮编辑：搜搜做题作业网作业帮分类：数学作业时间：2024/05/09 20:25:05

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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