广义积分 (下限-1,上限1) ∫1⼀x^2+4x+5 dx=??具体步骤怎么算呢!谢谢

2024-11-02 10:20:18
推荐回答(1个)
回答1:

∫(-1~1) 1/(x² + 4x + 5) dx
= ∫(-1~1) 1/[(x + 2)² + 1],公式∫ 1/(x²+a²) dx = (1/a)arctan(x/a)
= arctan(x + 2) |(-1~1)
= arctan(1 + 2) - arctan(2 - 1)
= arctan(3) - arctan(1)
= arctan(3) - π/4
≈ 0.463648