Question

（x^3+1）/（x^2+1）^2的不定积分

Answer 1

Let x = tanθ and dx = sec²θ dθ

∫ dx/(x²+1)^(3/2)

= ∫ (sec²θ)/(tan²θ+1)^(3/2) dθ

= ∫ (sec²θ)/(sec²θ)^(3/2) dθ

= ∫ (sec²θ)/(sec³θ) dθ

= ∫ cosθ dθ

= sinθ + C

= x/√(1+x²) + C

扩展资料

不定积分的公式

1、∫ a dx = ax + C，a和C都是常数

2、∫ x^a dx = [x^(a + 1)]/(a + 1) + C，其中a为常数且 a ≠ -1

3、∫ 1/x dx = ln|x| + C

4、∫ a^x dx = (1/lna)a^x + C，其中a > 0 且 a ≠ 1

5、∫ e^x dx = e^x + C

6、∫ cosx dx = sinx + C

7、∫ sinx dx = - cosx + C

8、∫ cotx dx = ln|sinx| + C = - ln|cscx| + C

Answer 2

 

Answer 3

超简单

追答

见44