∫ (2x^2+3)/{(x^2+1)^2} dx
问题描述：
∫ (2x^2+3)/{(x^2+1)^2} dx
答
设x=tant∫ (2x^2+3)/{(x^2+1)^2} dx=∫[2tan^2(t)+3]/sec^4(t)*sec^2(t)dt=∫[2sin^2(t)+3cos^2(t)]dt=∫[2+(1+cos2t)/2]dt=5t/2+sin2t/4+C=5arctanx/2+(1/2)x/(1+x^2)+C