求微分sin^2x*cos^5x*dx

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求微分sin^2x*cos^5x*dx求微分sin^2x*cos^5x*dx求微分sin^2x*cos^5x*dx∫(cosx)^5·(sinx)²dx=∫(cosx)^4·(sinx)&#

求微分sin^2x*cos^5x*dx
求微分sin^2x*cos^5x*dx

求微分sin^2x*cos^5x*dx
∫(cosx)^5·(sinx)²dx
=∫(cosx)^4·(sinx)²d(sinx)
=∫[(1-sinx)²]²(sinx)²d(sinx)
=∫(sin³x-2sin²x+sinx)² d(sinx)
=∫[(sinx)^6+4(sinx)^4+sin²x-4(sinx)^5-4sin³x+2(sinx)^4 ]d(sinx)
=1/7·(sinx)^7+4/5·(sinx)^5+1/3·sin³x-2/3·(sinx)^6-(sinx)^4+2/5·(sinx)^5+C
=1/7·(sinx)^7+6/5·(sinx)^5+1/3·sin³x-2/3·(sinx)^6-(sinx)^4+C