不定积分∫xarctanx^2/1+x^4不好意思没打全应该是∫xarctanx^2/1+x^4dx

Question

不定积分∫ xarctanx^2/1+x^4
不好意思没打全 应该是 ∫ xarctanx^2/1+x^4 dx

Answer 1

∫ x • arctan(x²)/(1 + x⁴) dx
= (1/2)∫ arctan(x²)/[1 + (x²)²] d(x²)
= (1/2)∫ arctan(x²) d[arctan(x²)]
= (1/2) • [arctan(x²)]²/2 + C
= (1/4)[arctan(x²)]² + C
都只是些凑微分的简单步骤：
x dx = d(x²/2)
1/(1 + x²) dx = d(arctanx)