搜搜考试网高数求微分谢了∫（t-sint）^2sintdt
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高数求微分
谢了∫（t-sint）^2sintdt
谢了∫（t-sint）^2sintdt
∫（t-sint）^2sintdt
=∫(t^2sint+sint^2sint-2tsint^2)dt
=∫t^2sintdt+∫(1-cost^2)sintdt-2∫tsint^2dt
=-∫t^2dcost-∫(1-cost^2)dcost-∫t*(1-cos2t)dt
=-t^2cost+∫2costdt-cost+cost^3/3-t^2/2+∫tdsin2t
=-t^2cost+2sint-cost+cost^3/3-t^2/2+tsin2t-∫sin2tdt
=-t^2cost+2sint-cost+cost^3/3-t^2/2+tsin2t-1/2*sin2t^2
=∫(t^2sint+sint^2sint-2tsint^2)dt
=∫t^2sintdt+∫(1-cost^2)sintdt-2∫tsint^2dt
=-∫t^2dcost-∫(1-cost^2)dcost-∫t*(1-cos2t)dt
=-t^2cost+∫2costdt-cost+cost^3/3-t^2/2+∫tdsin2t
=-t^2cost+2sint-cost+cost^3/3-t^2/2+tsin2t-∫sin2tdt
=-t^2cost+2sint-cost+cost^3/3-t^2/2+tsin2t-1/2*sin2t^2
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∫cost/(sint^2) dt =∫dsint/sint^2 =-1/sint + C
∫sint/(cost+sint)dt