求∫1/(x2+2x+3)dx

求∫1/(x²+2x+3)dx
【正确答案】：1/√2arctan(x+1)/√2+C ∫1/(x²+2x+3)dx =∫[1/2+(x+1)²+1)]d(x+1) =1/√2∫1/{1+[(x+1)√2]²}d[(x+1)/√2] =1/√2arctan[(x+1)/√2]+C