1ã第äºç±»æ¢å
积åæ³
令t=â(x-1)ï¼åx=t^2+1ï¼dx=2tdt
åå¼=â«(t^2+1)/t*2tdt
=2â«(t^2+1)dt
=(2/3)*t^3+2t+C
=(2/3)*(x-1)^(3/2)+2â(x-1)+Cï¼å
¶ä¸Cæ¯ä»»æ常æ°
2ã第ä¸ç±»æ¢å
积åæ³
åå¼=â«(x-1+1)/â(x-1)dx
=â«[â(x-1)+1/â(x-1)]d(x-1)
=(2/3)*(x-1)^(3/2)+2â(x-1)+Cï¼å
¶ä¸Cæ¯ä»»æ常æ°
3ãåé¨ç§¯åæ³
åå¼=â«2xd[â(x-1)]
=2xâ(x-1)-â«2â(x-1)dx
=2xâ(x-1)-(4/3)*(x-1)^(3/2)+Cï¼å
¶ä¸Cæ¯ä½ ä»»æ常æ°
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