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â«ï¼1-3xï¼^6dx
=(-1/3)â«(1-3x)^6d(1-3x)
=-1/3*(1-3x)^7*(1/7)+C
=-1/21*ï¼1-3xï¼^7+Cã
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ä¾å¦â«(sinx)^4dx
=â«[(1/2)(1-cos2x]^2dx
=(1/4)â«[1-2cos2x+(cos2x)^2]dx
=(1/4)â«[1-2cos2x+(1/2)(1+cos4x)]dx
=(3/8)â«dx-(1/2)â«cos2xdx+(1/8)â«cos4xdx
=(3/8)â«dx-(1/4)â«cos2xd2x+(1/32)â«cos4xd4x
=(3/8)x-(1/4)sin2x+(1/32)sin4x+Cã
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ä¾å¦â«cscxdx
=â«1/sinxdx
=â«1/[2sin(x/2)cos(x/2)]dxï¼ä¸¤åè§å ¬å¼
=â«1/[sin(x/2)cos(x/2)]d(x/2)
=â«1/tan(x/2)*sec²(x/2)d(x/2)
=â«1/tan(x/2)d[tan(x/2)]ï¼æ³¨â«sec²(x/2)d(x/2)=tan(x/2)+C
=ln|tan(x/2)|+Cã