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Maverick
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12 votes
Accepted

Let $M$ be a non-zero $3\times 3$ matrix satisfying $M^3=O$

9 votes

What are the conditions on $a$ such that the polynomial $x^4-2ax^2+x+a^2-a$ has four distinct real roots?

7 votes

When A and B are of different order given the $\det(AB)$,then calculate $\det(BA)$

6 votes
Accepted

If $\alpha+\beta+\gamma=\pi$, then does $\sqrt{\sin\alpha}+\sqrt{\sin\beta}+\sqrt{\sin\gamma}$ reach its maximum when $\alpha=\beta=\gamma$?

6 votes
Accepted

Integrating $\int e^{\cos x} \cos(2x+\sin x)dx$

6 votes

Polynomial problem with vieta formulas

5 votes

How to evaluate the following limit $\lim_{n\to \infty} \prod_{k=0}^n \left(1+\delta^{2^{k}}\right)$?

4 votes

Prove that there exists some $c\in(-3,3)$ such that$ \ \ g(c) \cdot g''(c)<0$.

4 votes

in triangle ABC there satisfies equation: $\cos A \cos B+\sin A\sin B\sin C=1$, determine possible values of $C$

4 votes

Evaluate $\int_0^\pi \frac{\sin^2 nx}{\sin^2 x}dx$

4 votes

Range of function $f(x)=\sqrt{4-x^2}+\sqrt{x^2-1}$

4 votes
Accepted

Proving: $\int_0^\infty\left(\frac{\ln x}{x^2+2ax\cos(t)+a^2}\right)\rm{d}x=\frac{t\ln (a)}{a\sin (t)}$

4 votes
Accepted

Set of all real values of $a$ for which the equation $(a-4)\sec^4x+(a-3)\sec^2x+1=0, (a\ne4)$ has real solutions

4 votes

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

3 votes
Accepted

Find $\int_{0}^{1} \frac{4x^{3}-6x^{2}+8x-3}{(x^{2}-x+1)^2}dx$.

3 votes

Find the length of perpendicular as shown

3 votes
Accepted

Locus of vertex of moving parabola

3 votes

Prove that $a^2+b^2+16\ge ab+4a+4b$ for all $a, b$.

3 votes
Accepted

Integrate $\frac{\sin2x+2}{\sin2x+\cos2x+1}$ with respect to $x$

3 votes

Integrate $\frac{\sin2x+2}{\sin2x+\cos2x+1}$ with respect to $x$

3 votes
Accepted

Finding The Least Integer Value

2 votes

Eliminating $\theta$ from $x^2+y^2=\frac{x\cos3\theta+y\sin3\theta}{\cos^3\theta}$ and $x^2+y^2=\frac{y\cos3\theta-x\sin3\theta}{\cos^3\theta}$

2 votes

Inequality $\frac{1}{4}(e^{-4} + e^{-1}) \leq \int_1^2 e^{-x^2}dx \leq \frac{1}{2}(e^{-4}+e^{-1})$

2 votes

Solve of $\int \frac{dx}{\left(x^2+9\right)^2}$ with Partial Integration

2 votes

Integrating $\int e^{\cos x} \cos(2x+\sin x)dx$

2 votes
Accepted

Property of Medians and Cirumcircle

2 votes
Accepted

Initial value problem of $y'(x)=2\cdot\sqrt{|y(x)|}$

2 votes

How to find the integration of $\sin2\theta\sqrt{\tan\theta} \ d\theta$

2 votes

In how many ways can $2^5\times 3^7$ be factored into three setwise coprime integers?

2 votes
Accepted

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