Question

How can I evaluate $\lim_{n \rightarrow \infty} \int_n^\infty \frac{n^2 \arctan {\frac{1}{x}}}{x^2+n^2}\ dx$?

score 1.3k · Answer 1 · 2026-04-16 03:09:11

1.3k

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How can I evaluate $\lim_{n \rightarrow \infty} \int_n^\infty \frac{n^2 \arctan {\frac{1}{x}}}{x^2+n^2}\ dx$?

Published on 16 Apr 2026 - 3:09

score 106 · Answer 2 · 2026-04-12 14:02:37

106

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Two different answers of same indefinite integral

Published on 12 Apr 2026 - 14:02

score 169 · Answer 3 · 2026-04-17 00:32:46

169

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Evaluate $\int \frac{x\tan(x) \sec(x)}{(\tan(x)-x)^2}$

Published on 17 Apr 2026 - 0:32

score 193 · Answer 4 · 2026-04-16 18:29:42

193

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Integral in Adams Bashforth derivation

Published on 16 Apr 2026 - 18:29

score 202 · Answer 5 · 2026-04-17 00:15:05

202

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Justify an approximation of the first few decimals of $\int_1^\infty(\int_0^1\frac{dx}{-1+x^3+y^2})dy$

Published on 17 Apr 2026 - 0:15

score 4.6k · Answer 6 · 2026-04-13 19:38:54

4.6k

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maximum of iid exponential random variables

Published on 13 Apr 2026 - 19:38

score 39 · Answer 7 · 2026-04-13 23:14:36

39

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integration on a parametric curve

Published on 13 Apr 2026 - 23:14

score 64 · Answer 8 · 2026-04-15 06:28:03

64

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Changing integration order of $\int_{0}^{1}\int_{e^{y-1}}^{e^y} f(x,y)dxdy$

Published on 15 Apr 2026 - 6:28

score 45 · Answer 9 · 2026-04-15 12:05:50

45

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Average values of imaginary numbers using integrals, is this result valid or does it even make any sense ??

Published on 15 Apr 2026 - 12:05

score 72 · Answer 10 · 2026-04-09 03:35:34

72

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How to solve the following integral

Published on 09 Apr 2026 - 3:35

score 1.4k · Answer 11 · 2026-04-14 11:57:28

1.4k

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Integral of a piecewise function

Published on 14 Apr 2026 - 11:57

score 78 · Answer 12 · 2026-04-09 12:18:40

78

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Double integral with function in limit

Published on 09 Apr 2026 - 12:18

score 100 · Answer 13 · 2026-04-17 08:45:11

100

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Is $\lim_{n\to \infty}\int_0^{\pi/2} \frac{x^{\frac 1n}+\sin x}{\tan x+x^{\frac 1n}} dx=\int_0^{\pi/2} \frac{1+\sin x}{\tan x+1} dx=1.62..$?

Published on 17 Apr 2026 - 8:45

score 79 · Answer 14 · 2026-04-10 16:59:38

79

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derivative of an integral with respect to its upper limit

Published on 10 Apr 2026 - 16:59

score 39 · Answer 15 · 2026-04-24 23:44:00

39

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Calculating a complex line integral

Published on 24 Apr 2026 - 23:44

List Question

How can I evaluate $\lim_{n \rightarrow \infty} \int_n^\infty \frac{n^2 \arctan {\frac{1}{x}}}{x^2+n^2}\ dx$?

Two different answers of same indefinite integral

Evaluate $\int \frac{x\tan(x) \sec(x)}{(\tan(x)-x)^2}$

Integral in Adams Bashforth derivation

Justify an approximation of the first few decimals of $\int_1^\infty(\int_0^1\frac{dx}{-1+x^3+y^2})dy$

maximum of iid exponential random variables

integration on a parametric curve

Changing integration order of $\int_{0}^{1}\int_{e^{y-1}}^{e^y} f(x,y)dxdy$

Average values of imaginary numbers using integrals, is this result valid or does it even make any sense ??

How to solve the following integral

Integral of a piecewise function

Double integral with function in limit

Is $\lim_{n\to \infty}\int_0^{\pi/2} \frac{x^{\frac 1n}+\sin x}{\tan x+x^{\frac 1n}} dx=\int_0^{\pi/2} \frac{1+\sin x}{\tan x+1} dx=1.62..$?

derivative of an integral with respect to its upper limit

Calculating a complex line integral

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