第1988题：一种题型
用上一题的方法计算不定积分
∫dx(x2+1)(x2+3)\int \dfrac{dx}{(x^2+1)(x^2+3)}∫(x2+1)(x2+3)dx .
A. 12ln∣x2+1x2+3∣\dfrac{1}{2} \ln \Big | \dfrac{x^2+1}{x^2+3} \Big |21ln∣∣∣x2+3x2+1∣∣∣ +C+C+C
B. 15arctanx2+1x2+3\dfrac{1}{5} \arctan \dfrac{x^2+1}{x^2+3} 51arctanx2+3x2+1 +C+C+C
C. 12arctan(x2)\dfrac{1}{2} \arctan (x^2) 21arctan(x2) −arctanx2+33+C-\arctan \dfrac{x^2+3}{\sqrt{3}}+C−arctan√3x2+3+C
D. 12arctanx\dfrac{1}{2} \arctan x21arctanx −123arctanx3+C-\dfrac{1}{2\sqrt{3}} \arctan \dfrac{x}{\sqrt{3}} +C−2√31arctan√3x+C
