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Zenix
  • Member for 4 years, 8 months
  • Last seen more than a month ago
5 votes
1 answer
104 views

Number of rational roots

5 votes
3 answers
371 views

Integrate $\int {\dfrac{x^2+\left(n-1\right)n}{\left(x\sin x+n\cos x\right)^2}}dx $

5 votes
2 answers
131 views

How to solve this integral equation

5 votes
3 answers
368 views

If $\mathrm{M,N}$ are $3\times 2, 2 \times 3$ matrices such that $\mathrm{MN}=$ is given. Then $\mathrm{det(NM)}$ is?

4 votes
1 answer
112 views

Proving inequality $(a^2 + b^2)^3 \ge 32(a^3 + b^3)(ab - a - b)$

4 votes
3 answers
152 views

Evaluating $\sum_{r=1}^{3n-1}\dfrac{(-1)^{r-1}\cdot r}{\binom{3n}r}$

3 votes
1 answer
1k views

Evaluate $\int\limits_{-1/8}^{1/8}\arccos\left(x^2+5x\right)\ dx$

3 votes
2 answers
526 views

Number of possible polynomials

3 votes
1 answer
121 views

Evaluate the integral $\int_0^\infty\dfrac{x}{\sqrt{x^5+1}}dx$

3 votes
1 answer
46 views

Least value of $\mid\{I + \lambda A^2\}\mid$

3 votes
1 answer
104 views

Proof of inequality in triangle

2 votes
1 answer
134 views

Number of integral solutions of polynomial

2 votes
2 answers
347 views

Integrate $\int_{0}^{\pi/2}{\frac{x\cos\left(x\right)-\sin\left(x\right)}{\sin\left(x\right)+x^2}}dx$

2 votes
1 answer
95 views

Proving $\sum_{r=0}^{n-1} (-1)^r \cos^n{\left(\frac{r\pi}{n}\right)}=\frac{n}{2^{n-1}}$

2 votes
3 answers
342 views

Let $A=\{1,2,3,...,9\}$ and $f:A \rightarrow A$ is a bijection such that $(fofofo\cdots n$ times) $=f$ but others are not identical to $f$

2 votes
1 answer
974 views

Four points in space, satisfying the conditions

2 votes
1 answer
86 views

Find the sum of infinite series $\cos{\frac{\pi}{3}}+\frac{\cos{\frac{2\pi}{3}}}{2}+..$

2 votes
2 answers
54 views

If $a_1a_2 = 1, a_2a_3 = 2, a_3a_4 = 3 \cdots$ and $ \lim_{n \to \infty} \frac{a_n}{a_{n+1}} = 1$, find $|a_1|$

1 vote
3 answers
49 views

$\sum_{r=0}^{19} (r+1)^4 \binom{20}{r+1}=\lambda. \, 2^{16}$

1 vote
0 answers
99 views

Question on Rolle's Theorem

1 vote
1 answer
468 views

Meaning of $\max{f(x)}$ in a given range

1 vote
1 answer
84 views

Evaluate $\frac{\binom{n}{0}}{m!}+n\cdot\frac{\binom{n}{1}}{(m+1)!}+n(n-1)\cdot\frac{\binom{n}{2}}{(m+2)!}+\ldots$

1 vote
3 answers
178 views

Integrate $\int_{0}^{\infty}{\frac{(x^2+4)\ln(x)}{x^4+16}}dx$

1 vote
1 answer
353 views

Sum of square distances from a point to the sides of a regular polygon

0 votes
2 answers
95 views

Find the infinite product [closed]

0 votes
1 answer
47 views

Finding $\lim_{x\rightarrow \infty} g(x)$, when $\lim_{x\rightarrow \infty} f(x)=0$ is given.

0 votes
3 answers
73 views

Prove that solution set of $sz+t\bar{z}+r=0$ can not have exactly 10 Allegra