Question

Smarter way to solve $ \int_0^1\arctan(x^2)\,dx$

score 215 · Answer 1 · 2020-02-12 16:50:11

215

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Smarter way to solve $ \int_0^1\arctan(x^2)\,dx$

Published on 12 Feb 2020 - 16:50

score 124 · Answer 2 · 2026-03-29 22:33:07

124

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Limit of $x(\sqrt{x^2+1}-\sqrt[3]{x^3+1})$

Published on 29 Mar 2026 - 22:33

score 685 · Answer 3 · 2020-02-13 03:26:42

685

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Let A be an $n*n$ matrix. a). suppose $A^2=0$ (zero matrix).

Published on 13 Feb 2020 - 3:26

score 77 · Answer 4 · 2026-03-25 19:07:21

77

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Integral inequality $\int_{\frac{1}{2}}^{1}x^x\operatorname{W(x)}\operatorname{dx}<\frac{1}{9c-15}$

Published on 25 Mar 2026 - 19:07

score 96 · Answer 5 · 2020-02-13 21:34:39

96

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How to show that $\theta(A):=A\cup\mathscr{der}(A)$ is a kuratowski operator?

Published on 13 Feb 2020 - 21:34

score 827 · Answer 6 · 2020-02-15 05:18:44

827

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Let $n$ be a natural number. if $|n - 1| + |n + 1| ≤ 1$, then $|n^2 - 1| ≤ 4$

Published on 15 Feb 2020 - 5:18

score 254 · Answer 7 · 2020-02-16 01:08:51

Alternative Proof: If $(x_n)$ is bounded and diverges, then there exist two subsequences of $(x_n)$ that converge to diﬀerent limits

score 173 · Answer 8 · 2020-02-16 18:14:20

173

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If $|z_1+z_2+z_3|=|z_2+z_3|=|z_1|$ find $\frac{z_1}{z_2+z_3}$

Published on 16 Feb 2020 - 18:14

score 90 · Answer 9 · 2020-02-18 22:02:48

90

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Let $\lim_{n\to\infty}(a_n)=\infty$ and $(b_n)_{n\in\mathbb N}$ be bounded. Prove that $\lim_{n\to\infty}(a_n+b_n)=\infty$.

Published on 18 Feb 2020 - 22:02

score 213 · Answer 10 · 2026-03-25 11:08:06

213

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Simpler proof for tensor invariance

Published on 25 Mar 2026 - 11:08

score 79 · Answer 11 · 2020-02-19 07:33:35

79

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If $A+A^t=I$ and $\lambda$ eigenvalue of $A$ then $\lambda=\frac{1}{2}+$ $i\alpha$

Published on 19 Feb 2020 - 7:33

score 218 · Answer 12 · 2026-04-01 05:05:23

218

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Proof about the invertibility of the power of a matrix

Published on 01 Apr 2026 - 5:05

score 124 · Answer 13 · 2026-04-01 04:13:00

124

Views

Show that $(\mathbb{Z}_{n} \times \mathbb{Z}_{n} , +)$ is not isomorphic to $ (\mathbb{Z}_{n^{2}} , +)$

Published on 01 Apr 2026 - 4:13

score 56 · Answer 14 · 2026-03-25 11:10:35

56

Views

Direct proof using telescoping series for $a_n = 1 + 2^{2-n}$

Published on 25 Mar 2026 - 11:10

score 197 · Answer 15 · 2026-03-27 07:50:42

197

Views

Evaluating $\int_0^1\frac{\ln x\operatorname{Li}_2(x)\ln(1-x/2)}{x}\ dx$

Published on 27 Mar 2026 - 7:50

List Question

Smarter way to solve $ \int_0^1\arctan(x^2)\,dx$

Limit of $x(\sqrt{x^2+1}-\sqrt[3]{x^3+1})$

Let A be an $n*n$ matrix. a). suppose $A^2=0$ (zero matrix).

Integral inequality $\int_{\frac{1}{2}}^{1}x^x\operatorname{W(x)}\operatorname{dx}<\frac{1}{9c-15}$

How to show that $\theta(A):=A\cup\mathscr{der}(A)$ is a kuratowski operator?

Let $n$ be a natural number. if $|n - 1| + |n + 1| ≤ 1$, then $|n^2 - 1| ≤ 4$

Alternative Proof: If $(x_n)$ is bounded and diverges, then there exist two subsequences of $(x_n)$ that converge to diﬀerent limits

If $|z_1+z_2+z_3|=|z_2+z_3|=|z_1|$ find $\frac{z_1}{z_2+z_3}$

Let $\lim_{n\to\infty}(a_n)=\infty$ and $(b_n)_{n\in\mathbb N}$ be bounded. Prove that $\lim_{n\to\infty}(a_n+b_n)=\infty$.

Simpler proof for tensor invariance

If $A+A^t=I$ and $\lambda$ eigenvalue of $A$ then $\lambda=\frac{1}{2}+$ $i\alpha$

Proof about the invertibility of the power of a matrix

Show that $(\mathbb{Z}_{n} \times \mathbb{Z}_{n} , +)$ is not isomorphic to $ (\mathbb{Z}_{n^{2}} , +)$

Direct proof using telescoping series for $a_n = 1 + 2^{2-n}$

Evaluating $\int_0^1\frac{\ln x\operatorname{Li}_2(x)\ln(1-x/2)}{x}\ dx$

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