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sEC x的积分怎么求

∫ secx dx = ∫ secx • (secx + tanx)/(secx + tanx) dx = ∫ (secxtanx + sec²x)/(secx + tanx) dx = ∫ d(secx + tanx)/(secx + tanx) = ln|secx + tanx| + C 扩展资料: 常用的积分公式有 (1)f(x)->∫f(x)dx (2)k->kx (3)x^n->[...

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(tanx)'=sec²x ∫sec²xdx=tanx+C

用S代表积分号. Ssec^3(x)dx =Ssec(x)dtan(x) =sec(x)tan(x)-Ssec^3(x)sin^2(x)dx =sec(x)tan(x)-Ssec^3(x)(1-cos^2(x))dx =sec(x)tan(x)-Ssec^3(x)dx+Ssec(x)dx. 于是 2 Ssec^3(x)dx=sec(x)tan(x+Ssec(x)dx. 而 Ssec(x)dx=ln|tan(Pi/4-x/2)|+C....

首先求∫sec^3(x) dx:记I=∫sec^3(x) dx,则I =∫sec(x)*sec^2(x) dx =∫sec(x)*[tan(x)]' dx =sec(x)*tan(x)-∫[sec(x)]'*tan(x) dx =sec(x)*tan(x)-∫[sec(x)*tan(x)]*tan(x) dx =sec(x)*tan(x)-∫sec(x)*tan^2(x) dx =sec(x)*tan(x)-∫sec(x)*[sec^2...

∫sec³xdx =∫secxd(tanx) =secxtanx-∫tanxd(secx) =secxtanx-∫tan²xsecxdx =secxtanx-∫(sec²x-1)secxdx =secxtanx+∫secxdx-∫sec³xdx =secxtanx+ln|secx+tanx|-∫sec³xdx 所以∫sec³xdx=(1/2)secxtanx+(1/2)ln|secx+t...

∫ sec³xdx =∫ secxd(tanx) =secxtanx-∫ tan²xsecxdx =secxtanx-∫ (sec²x-1)secxdx =secxtanx-∫ sec³xdx+∫secxdx =secxtanx-∫ sec³xdx+ln|secx+tanx| 将-∫ sec³xdx移动等式左边与左边合并,除去系数(别忘记要留常...

解:∫xsec²xdx=∫xdtanx =xtanx-∫tanxdx =xtanx-∫sinx/cosx dx =xtanx+∫dcosx/cosx =xtanx+㏑|cosx|+C

注意基本求导公式 (tanx)'=sec²x 所以在这里得到 ∫ tan²x *sec²x dx =∫ tan²x d(tanx) = 1/3 *(tanx)^3 +C,C为常数

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