vict20062008
幼苗
共回答了17个问题采纳率:94.1% 举报
∫x^2(x^3+4)^5dx
=1/3∫(x^3+4)^5dx^3
=1/3∫(x^3+4)^5d(x^3+5)
=1/3*1/6*(x^3+4)^6+C
=(x^3+4)^6/18+C
∫e^2x/√(2e^x+1)dx
=∫e^x/√(2e^x+1)*e^xdx
=∫e^x/√(2e^x+1)de^x
=1/2*∫e^x/√(2e^x+1)d2e^x
=1/2*∫e^x/√(2e^x+1)d(2e^x+1)
=1/2*(-1/2+1)∫e^xd√(2e^x+1)
=1/4[√(2e^x+1)*e^x-∫√(2e^x+1)*de^x]
=1/4[√(2e^x+1)*e^x-1/2*∫√(2e^x+1)*d(2e^x+1)]
=1/4[√(2e^x+1)*e^x-1/2*(1/2+1)(2e^x+1)^(1/2+1)]+C
=√(2e^x+1)*e^x/4-3(2e^x+1)^(3/2)/16+C
∫sin(1/x)/x^2dx
=-∫sin(1/x)d(1/x)
=-(-cos(1/x))+C
=cos(1/x)+C
1年前
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