success0806
春芽
共回答了24个问题采纳率:83.3% 举报
1.∫(tan x)^2 dx
=∫sin^2x/cos^2xdx
=∫(1-cos^2x)/cos^2xdx
=∫sec^2x-1dx
=tanx-x+C
2.∫(tan x)^2 * (sec x)^2 dx
=∫sin^2x/cos^4xdx
=-∫sinx/cos^4xdcosx
=(1/3)sinxd(1/cos^3x)
=sinx/(3cos^3x)-∫(1/cos^3x)dsinx
=sinx/(3cos^3x)-∫sec^2xdx
=sinx/(3cos^3x)-tanx+C
3.∫(tan x)^3 * (sec x)^2 dx
=∫sin^3x/cos^5xdx
=∫(cos^2x-1)/cos^5xdcosx
=1/(4cos^4x)-1/(2cos^2x)+C
4.∫tan x / ((cos x) + 1) dx
=∫sinx/[cosx(1+cosx)]dx
=∫1/(1+cosx)-1/cosxdcosx
=ln(1+cosx)-ln|cosx|+C
1年前
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