Question

Integral $\int_{-\infty}^{\infty} \frac{1}{a^2 x^2 + 1} \frac{1}{x^2 + 1} \mathrm{d}x,\quad a \in \mathbb{R}$

score 112 · Answer 1 · 2026-04-06 11:11:20

112

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Integral $\int_{-\infty}^{\infty} \frac{1}{a^2 x^2 + 1} \frac{1}{x^2 + 1} \mathrm{d}x,\quad a \in \mathbb{R}$

Published on 06 Apr 2026 - 11:11

score 3.6k · Answer 2 · 2026-04-12 12:31:44

3.6k

Views

What is a refinement of a partition (Riemann integral)?

Published on 12 Apr 2026 - 12:31

score 61 · Answer 3 · 2026-04-13 23:01:54

61

Views

Solving differential equation using a pair of integrals as helper

Published on 13 Apr 2026 - 23:01

score 48 · Answer 4 · 2026-04-11 00:38:49

48

Views

Study the convergence and then calculate the improper integrals

Published on 11 Apr 2026 - 0:38

score 73 · Answer 5 · 2026-03-25 06:11:23

73

Views

Improper integral and moment-generating function of a function of exponential distributions

Published on 25 Mar 2026 - 6:11

score 136 · Answer 6 · 2026-04-08 07:25:06

136

Views

calculate a limit of a succession of functions

Published on 08 Apr 2026 - 7:25

score 72 · Answer 7 · 2026-04-12 11:22:08

72

Views

Study the convergence and calculate the improper integral

Published on 12 Apr 2026 - 11:22

score 109 · Answer 8 · 2026-04-12 04:52:22

109

Views

Why in this definition of Riemann integral isn't required that the mesh gets smaller?

Published on 12 Apr 2026 - 4:52

score 189 · Answer 9 · 2026-04-11 14:54:30

189

Views

Leibniz integral rule and Fundamental theorem of calculus

Published on 11 Apr 2026 - 14:54

score 78 · Answer 10 · 2026-04-16 20:01:40

78

Views

Prove the identity $\int_{2a-1}^{2a} f(x)dx = 2 \int_{a}^{\infty}g(x)dx$

Published on 16 Apr 2026 - 20:01

score 93 · Answer 11 · 2026-04-09 19:58:55

93

Views

Difficulty with Proof of Integrability

Published on 09 Apr 2026 - 19:58

score 141 · Answer 12 · 2026-04-10 15:00:55

141

Views

intergration between limits

Published on 10 Apr 2026 - 15:00

score 79 · Answer 13 · 2026-04-17 11:34:14

79

Views

$\int_0^\infty f(t)^2 x(t)^2 dt \le \int^1_0 f(t)^2 dt?$

Published on 17 Apr 2026 - 11:34

score 47 · Answer 14 · 2026-04-12 07:31:25

47

Views

Convolution with even function

Published on 12 Apr 2026 - 7:31

score 185 · Answer 15 · 2026-04-11 13:17:59

185

Views

Integral to partial sum

Published on 11 Apr 2026 - 13:17

List Question

Integral $\int_{-\infty}^{\infty} \frac{1}{a^2 x^2 + 1} \frac{1}{x^2 + 1} \mathrm{d}x,\quad a \in \mathbb{R}$

What is a refinement of a partition (Riemann integral)?

Solving differential equation using a pair of integrals as helper

Study the convergence and then calculate the improper integrals

Improper integral and moment-generating function of a function of exponential distributions

calculate a limit of a succession of functions

Study the convergence and calculate the improper integral

Why in this definition of Riemann integral isn't required that the mesh gets smaller?

Leibniz integral rule and Fundamental theorem of calculus

Prove the identity $\int_{2a-1}^{2a} f(x)dx = 2 \int_{a}^{\infty}g(x)dx$

Difficulty with Proof of Integrability

intergration between limits

$\int_0^\infty f(t)^2 x(t)^2 dt \le \int^1_0 f(t)^2 dt?$

Convolution with even function

Integral to partial sum

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