解得A=6,B=-3,C=-3,D=-3 原式 ∫c 33t+3 1+t1+ 6Int-3In(1+t-In(1+t)-3arctant+C 2 x-3In(1+e6)-In(1+e3)-3arctan e6 +C.解得 A = 6, B = −3, C = −3, D = −3. dt t t t t ) 1 3 3 1 6 3 ( 2 + + − + = − 原式  = t − + t − ln(1 + t ) − 3arctan t + C 2 3 6ln 3ln(1 ) 2 ln(1 ) 3arctan . 2 3 3 ln(1 ) 6 3 6 x e e e C x x x = − + − + − +