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〈〔(1+x)/xDx

〈〔(1+x^2) /x dx let x= tanu dx=(secu)^2 du 〈〔(1+x^2) /x dx =〈(secu)^3/tanu du =〈cscu dtanu =cscu .tanu + 〈cscu du =cscu .tanu + ln|cscu-cotu| + C =〔(1+x^2) + ln| 〔(1+x^2)/x - 1/x | + C

綜〔(1+x)=t夸x=t²-1 〈xdx/〔(1+x) =〈[(t²-1)/t]d(t²-1) =〈[(t²-1),2t/t]dt =2〈(t²-1)dt =⅔t³-2t +C =⅔(t²-3)t +C =⅔(x+1-3)〔(1+x) +C =⅔(x-2)〔(1+x) +C

綜y=〔(1+x),夸x=y^2-1 圻塀=〈y/(2-y^2)d(y^2-1) =2〈y^2/(2-y^2)dy =-2〈[1+2/(y^2-2)]dy =-2〈dy-〔2〈[1/(y-〔2)-1/(y+〔2)]dy =-2y-〔2[ln(y-〔2)-ln(y+〔2)]+C =-2y-〔2ln[(y-〔2)/(y+〔2)]+C =-2〔(1+x)-〔2ln[(〔(1+x)-〔2)/(〔(1+x)+〔2)]+C

綜〔x=t 椎担x=t²dx=2t dt 軸t議貧和淮2才0 侭參誼欺 圻持蛍=〈 t *2t /(1+t^3) dt =〈 2t² /(1+t^3) dt =〈 2/3(1+t^3) d(1+t^3) =2/3 *ln|1+t^3| 旗秘t 議貧和2才0 =2/3 *(ln9 -ln1) =2/3 *ln(3^2)=4/3 *ln3

[x(1-x+x^2)]-(1/[x(1+x)] =(1/[(x-1/〈〔[(1-x)/.;3)〈dx/6)〈dx^2/3)〈dx/3)〈xdx/6)〈dx/.=(2/|x| ]+C 〈dx/3)〈(1+x)dx/3)〈dx/[(1-sinu)(1+sinu)] =tanu-ln[|1+sinu|/.;2)^2+3/3)ln|x|+;[x^2(1-x+x^2)]+(1/(1+x)] dx/.;4]-(1/(1+x)]=(1-cosu)/3)〈xdx/...

基 咀葎持蛍痕方y=f(x)=1/x頁郡曳箭痕方贋壓曾屶 侭參x0脅勣深打 x>0扮持蛍誼lnx+C x

圻籾頁焚担亜 委圻籾壅勧和 葎低盾基和

綜〔[(1-x²)/(1+x²)]=t夸x²=(1-t²)/(1+t²) 〈〔[(1-x²)/(1+x²)]xdx =½〈〔[(1-x²)/(1+x²)]d(x²) =½〈td[(1-t²)/(1+t²)] =½t(1-t²)/(1+t²) -½〈[(1-t...

盾 圻塀=Inx 錬李斤低嗤逸廁 音峡弖諒

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