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Jia Ming جيا ميڠ's user avatar
Jia Ming جيا ميڠ's user avatar
Jia Ming جيا ميڠ's user avatar
Jia Ming جيا ميڠ
  • Member for 7 years, 7 months
  • Last seen more than a month ago
10 votes
5 answers
333 views

Ways to prove that $\int_0^\infty \frac{x^2 \ln(x)}{(1+x^2)^3} {\rm d}x = 0$.

9 votes
2 answers
302 views

Finding solutions to the diophantine equation $xy(x+y) = n$.

6 votes
2 answers
428 views

Continuous antiderivative of $\frac{1}{1+\cos^2 x}$ without the floor function.

5 votes
1 answer
235 views

Evaluating $ \int \frac1{5S_{8} - 9S_{10} + 7S_{12} - 2S_{14}} {\rm d}x$, where $S_n = \sin^n(x) + \cos^n(x)$

5 votes
2 answers
337 views

Frullani integral $\int_0^\infty \frac{\text{csch}(x)-\frac1x}{x} {\rm d}x$

4 votes
4 answers
234 views

Prove that $\int_0^{\frac{n\pi}{4}} \frac{1}{3\sin^4(x) + 3\cos^4(x) -1} dx = \frac{n\pi}{4} $

4 votes
3 answers
278 views

Proving a trigonometric identity by integration.

3 votes
3 answers
489 views

Prove that $\sqrt[8]5 > \sqrt[9]6 > \sqrt[10]7 > \cdots$

3 votes
2 answers
242 views

Definite integral $\int_0^{\pi/12} \left( \frac{e^x \cos(x)}{\cos(x+\frac\pi4)} \right)^2 {\rm d}x= e^{\pi/6} \cos \left( \frac\pi6 \right) - \frac12$

2 votes
1 answer
68 views

Approximating $\cos\left(\frac{\pi x}{2}\right)$ with $k\sqrt{1-x^2}$.

2 votes
1 answer
91 views

Tough integral from a falling clock. $\int_0^{2\pi} \sqrt{g^2t^2 + 2rgt\sin(t) + r^2} {\rm d}t$

2 votes
1 answer
99 views

$\int_0^\infty \frac{x^a\ln(x)}{(x^2-bx+1)^{a+1}}{\rm d}x = 0$?

2 votes
1 answer
42 views

Fallacious moving of powers resulting with a correct trigonometric series identity.

2 votes
2 answers
284 views

Proving that the common normal between any two smooth curves corresponds to a stationary point of their distance apart.

2 votes
1 answer
53 views

Confusion on ambiguity of antiderivatives.

1 vote
1 answer
818 views

Proving that the orthocentre of an acute triangle is its orthic triangle's incentre.

1 vote
2 answers
63 views

Proving that these two finite alternating series are equal.

1 vote
1 answer
97 views

$ \int \bigl| a\sin(x)+b\cos(x) \bigr| {\rm d}x = ? $

1 vote
4 answers
127 views

Finding interesting ways to solve $\int \frac{2\sinh(x)+1}{2\cosh(3x)} {\rm d}x$.

0 votes
1 answer
53 views

Misunderstanding regarding the Axiom of Union: "All of the elements of some elements of"

0 votes
2 answers
270 views

Limit of sequence in which each term is the average of its preceding k terms.