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A-Level Student
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35 votes
5 answers
2k views

What other tricks and techniques can I use in integration?

28 votes
2 answers
1k views

Evaluate $\sqrt{x+\sqrt{{x^2}+\sqrt{{x^3}+\sqrt{{x^4}...}}}}$

19 votes
2 answers
920 views

How do we know that the Sine function has no Non-Real Roots?

16 votes
6 answers
549 views

If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$ [duplicate]

15 votes
2 answers
480 views

Evaluate $\sum\limits_{n=1}^{\infty}\frac{1}{n^3}\binom{2n}{n}^{-1}$. [duplicate]

13 votes
0 answers
278 views

Is $\sum_{r=1}^nrx^{r-1}$ always irreducible (over the integers)? [duplicate]

11 votes
4 answers
227 views

Graphing $f(2-x)$

10 votes
5 answers
517 views

Evaluate $\int_{0}^{\pi} \frac{x\coth x-1}{x^2}dx$

9 votes
4 answers
423 views

Why doesn't $\int\lfloor {x}\rfloor~dx=x\lfloor x\rfloor +C$?

8 votes
6 answers
425 views

A very interesting question: intersection point of $x^y=y^x$

7 votes
1 answer
159 views

Number of solution sets to $\frac{1}{a_1}+\frac{1}{a_2}+\cdots+\frac{1}{a_n}=1,~~a_1,a_2,\ldots,a_n\in\mathbb{N}$

5 votes
1 answer
71 views

Find the $x^2$ coefficient by induction of $\frac{\sin x}{x}$

5 votes
5 answers
160 views

Why isn't $x^2+x+1$ a factor of $x^{12}+x^6+1$?

5 votes
2 answers
137 views

Does $\int1+\sin^2x+\sin^4x+\sin^6x+...\text{dx}=\tan{x}$?

5 votes
4 answers
838 views

Why doesn't trig substitution work for definite integrals?

4 votes
3 answers
235 views

Limit $\lim _{x \to 0}\sqrt {x+\sqrt {x+\sqrt{x+\sqrt{x...}}}}=1$

4 votes
3 answers
189 views

Proof that any number is equal to $1$

4 votes
3 answers
268 views

How many Assumptions can I make in Proof by Induction?

4 votes
4 answers
623 views

Does L'Hopital's rule imply that $\lim_{x\to a}\frac{f'(x)}{g'(x)} = \lim_{x\to a}\frac{f(x)}{g(x)}$ always?

4 votes
7 answers
590 views

Challenging Integrals for High School Students

4 votes
0 answers
219 views

Closed form for Sum of Tangents with Angles in Arithmetic Progression

4 votes
0 answers
99 views

Is the matrix $\begin{pmatrix} \cosh^2 x & \cosh^2 x\\ -\sinh^2x&-\sinh^2x\end{pmatrix}$ significant?

3 votes
2 answers
75 views

Solve $\frac{dy}{dx}=\frac{y+y^2+x^2}{x}$

3 votes
1 answer
98 views

'Proof' that $f''(x)=\frac{f'(x)}{x}$

3 votes
9 answers
396 views

Prove that $\frac{d}{dx}e^x=e^x$

3 votes
2 answers
175 views

What does $f:\mathbb R \rightarrow \mathbb R$ mean?

3 votes
1 answer
106 views

Question on Fundamental Theorem of Calculus

3 votes
1 answer
77 views

Significance of $e^\pi$

3 votes
0 answers
104 views

Is this simple proof of the triangle inequality correct?

3 votes
1 answer
111 views

Prove that $\sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{F_kF_{k+1}}=\frac{1}{\phi}$.