Question

Find all $x \in \mathbb{R}$ such that $1+\sqrt{1-\frac{1}{x}}+\sqrt{x-\frac{1}{x}}=x^2$.

score 213 · Answer 1 · 2024-02-16 05:13:22

213

Views

Find all $x \in \mathbb{R}$ such that $1+\sqrt{1-\frac{1}{x}}+\sqrt{x-\frac{1}{x}}=x^2$.

Published on 16 Feb 2024 - 5:13

score 188 · Answer 2 · 2024-02-20 15:09:30

188

Views

Why doesn't substiuting work here?

Published on 20 Feb 2024 - 15:09

score 16 · Answer 3 · 2026-03-09 09:07:22

16

Views

Parametric curve substitution

Published on 09 Mar 2026 - 9:07

score 37 · Answer 4 · 2024-02-20 23:44:43

37

Views

What U substitution is being used here? (direct integral calculation of charge)

Published on 20 Feb 2024 - 23:44

score 23 · Answer 5 · 2024-03-05 13:25:27

23

Views

Estimating an integral via substitution

Published on 05 Mar 2024 - 13:25

score 73 · Answer 6 · 2026-03-26 01:34:59

73

Views

How is this property of definite integral derived?

Published on 26 Mar 2026 - 1:34

score 81 · Answer 7 · 2024-03-06 04:25:00

81

Views

Approach to evaluate the integral $\int \frac{1}{{x^3}\sqrt{x^2-a^2}}dx$ using basic substitution.

Published on 06 Mar 2024 - 4:25

score 52 · Answer 8 · 2024-03-09 18:09:41

52

Views

What is wrong with substituting a constant in a system of equations?

Published on 09 Mar 2024 - 18:09

score 48 · Answer 9 · 2026-03-28 10:56:10

48

Views

Textbook says to integrate a fraction using 'Taylor's formula'?

Published on 28 Mar 2026 - 10:56

score 63 · Answer 10 · 2026-03-26 17:30:16

63

Views

Trigonometric Substitutions related to Elliptic Integrals

Published on 26 Mar 2026 - 17:30

score 26 · Answer 11 · 2026-03-29 10:12:09

26

Views

Python sympy: Expressions with an undefined function whose value at zero is known

Published on 29 Mar 2026 - 10:12

score 46 · Answer 12 · 2024-03-30 14:02:14

46

Views

How should these types of integrals be solved? $\int\frac{1}{y}\frac{1}{\ln y}$

Published on 30 Mar 2024 - 14:02

score 71 · Answer 13 · 2024-03-31 01:42:29

71

Views

Evaluate $\int{\frac{1}{x^3}}$ using u-sub.

Published on 31 Mar 2024 - 1:42

score 117 · Answer 14 · 2026-03-26 09:40:26

117

Views

Symmetric and homogeneous three variable inequality with radicals.

Published on 26 Mar 2026 - 9:40

score 399 · Answer 15 · 2026-03-25 06:30:34

399

Views

Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$

Published on 25 Mar 2026 - 6:30

List Question

Find all $x \in \mathbb{R}$ such that $1+\sqrt{1-\frac{1}{x}}+\sqrt{x-\frac{1}{x}}=x^2$.

Why doesn't substiuting work here?

Parametric curve substitution

What U substitution is being used here? (direct integral calculation of charge)

Estimating an integral via substitution

How is this property of definite integral derived?

Approach to evaluate the integral $\int \frac{1}{{x^3}\sqrt{x^2-a^2}}dx$ using basic substitution.

What is wrong with substituting a constant in a system of equations?

Textbook says to integrate a fraction using 'Taylor's formula'?

Trigonometric Substitutions related to Elliptic Integrals

Python sympy: Expressions with an undefined function whose value at zero is known

How should these types of integrals be solved? $\int\frac{1}{y}\frac{1}{\ln y}$

Evaluate $\int{\frac{1}{x^3}}$ using u-sub.

Symmetric and homogeneous three variable inequality with radicals.

Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$

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