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Emmanuel José García

Member for 8 years, 1 month
Last seen this week

geometriadominicana.blogspot.…

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integration

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Questions

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13

The theoretical importance of the half-angle formulas

May 22, 2022

11

Trigonometric formula for solving quadratic equations

Jan 13

9

Showing $\int_{-1}^{1} \frac{125}{12}\sqrt[10]{\frac{1 + x}{1 - x}} (x^2 - x) \, dx = \phi\pi$

Mar 28

9

Generalization of the law of tangents for a cyclic quadrilateral

Mar 16, 2022

5

Generalization of two formulae and an alternative proof of Bretschneider's formula

Aug 22, 2020

Answers

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6

Is there a definite integral that yields $e^\pi$ or $e^{-\pi}$ in a non trivial way?

Feb 11

2

Evaluating $\int x \sqrt{x^2 - x}\ dx$

Jul 23

2

How to evaluate $\int\sqrt{\frac{5+x}{7+x}}dx$?

Jul 6

2

What is $ \int_{0}^{\frac{1}{\sqrt{3}}} \sqrt{x + \sqrt{x^2 + 1}} \rm{d}x$?

Jul 2

1

Sum of the Volumes of Two Tetrahedra Obtained by Reflection Equals the Volume of the Reference Tetrahedron

Jul 25, 2023

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integration

12

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posts

calculus

6

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14

posts

exponentiation

6

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1

post

indefinite-integrals

5

Score

12

posts

geometry

1

Score

13

posts

Reputation

+10

Showing $\int_{-1}^{1} \frac{125}{12}\sqrt[10]{\frac{1 + x}{1 - x}} (x^2 - x) \, dx = \phi\pi$

+20

Evaluating $\int x \sqrt{x^2 - x}\ dx$

+10

Integrals of the form $\int f\left(x,\frac{\sqrt{x+m}}{\sqrt{x+n}}\right)\,dx$

+10

Showing $\int_{-1}^{1}\ln \left( \frac{x+1}{x-1} \right) \left( x - \sqrt{x^2 - 1} \right) \, dx=\frac{\pi^2 + 4}{2}$

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