User Emmanuel José García - Mathematics Stack Exchange

6 votes

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

answered Feb 11 at 19:06

2 votes

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

answered Jul 6 at 14:58

2 votes

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

answered Jul 2 at 14:25

1 vote

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

answered yesterday

1 vote

Find the integral $\int\frac{\sqrt{x-1}-\sqrt{x+1}}{\sqrt{x-1}-3\sqrt{x+1}}dx$

answered Mar 21 at 14:05

1 vote

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

answered Jul 25, 2023 at 16:25

0 votes

Indefinite integral that Wolfram Alpha can't solve

answered Feb 8 at 11:24

0 votes

Prove concurrency (probably using Carnot's Theorem)

answered Jul 30, 2016 at 3:52

0 votes

How can I understand and prove the "sum and difference formulas" in trigonometry?

answered May 2, 2023 at 11:28

0 votes

Interesting and unexpected applications of $\pi$

answered Feb 11 at 21:13

0 votes

Evaluating $\int x^2 \sqrt{x^2-1} dx$

answered May 10 at 18:47

0 votes

Integrate $\int \sqrt{\frac{x}{x+1}}dx$

answered Jul 5 at 16:05

0 votes

Evaluating $\displaystyle\int_0^1\frac{\sqrt{1-y^2}}{1+y^2}dy$ without trig substitution

answered Apr 12 at 13:11

0 votes

Evaluating the indefinite integral $\int\log\!\left(x+\sqrt{x^2-1}\right)\!dx$

answered Jun 9 at 14:32

0 votes

Evaluation of $\int\frac{1}{x+ \sqrt{x^2-x+1}}dx$

answered Jul 19 at 15:06

0 votes

Is it possible to evaluate $\int\frac{dx}{\sqrt{x^2+4}}$ without using trigonometric substitution?

answered Apr 8 at 18:16

0 votes

What other tricks and techniques can I use in integration?

answered Apr 5 at 13:53

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17 Answers

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

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

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

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

Find the integral $\int\frac{\sqrt{x-1}-\sqrt{x+1}}{\sqrt{x-1}-3\sqrt{x+1}}dx$

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

Indefinite integral that Wolfram Alpha can't solve

Prove concurrency (probably using Carnot's Theorem)

How can I understand and prove the "sum and difference formulas" in trigonometry?

Interesting and unexpected applications of $\pi$

Evaluating $\int x^2 \sqrt{x^2-1} dx$

Integrate $\int \sqrt{\frac{x}{x+1}}dx$

Evaluating $\displaystyle\int_0^1\frac{\sqrt{1-y^2}}{1+y^2}dy$ without trig substitution

Evaluating the indefinite integral $\int\log\!\left(x+\sqrt{x^2-1}\right)\!dx$

Evaluation of $\int\frac{1}{x+ \sqrt{x^2-x+1}}dx$

Is it possible to evaluate $\int\frac{dx}{\sqrt{x^2+4}}$ without using trigonometric substitution?

What other tricks and techniques can I use in integration?