Please help me to determine $\alpha$ and $p$, such that the integral $$ I = \iint_G \frac{1}{(x^{\alpha}+y^3)^p} \ dx dy $$ converges, where $G = {x>0,...

For this equation $$3x^2 + y^3 + 9 = -2xy,$$ I checked on wolfram alpha and it doesn't seem to have an explicit form where $y$ is isolated and equals...

Integrate $\int x \, \tan^{-1} (x) \, dx$ My Attempt: \begin{align} \int x \, \tan^{-1} (x) \, dx &= \int x \, \tan^{-1} (x) \, dx \\ &= \dfrac {x...

Let $A \in M_n(\mathbb{C})$ with $p_A(x)=(-1)^n\cdot (x-λ_1)\dots(x-λ_n)$ it's characteristic polynomial. Prove that $p_{A^2}(x)=(-1)^n\cdot (x-λ_1^2...

I'm finding points of intersection between two functions, $y = \tan(x)$ and $y = 2\sin(x)$, which are bound between $-\pi/3$ and $\pi/3$. Solving for...

I have been trying to solve this equation for over a week now: $$\tan5x-2\tan3x=\tan3x\tan5x$$ I found one solution $x=k\pi$ but I cannot prove that this ...

Here is the question $\log \left (\sqrt{x^3\sqrt{y^5\sqrt{z}}} \,\right) $ My work: http://i.imgur.com/GBcuzEI.jpg

How to factor the equation: $$x^2 + 2xy + y^2 - 2x - 2y - 15 = 0$$ I tried to solve this equation several times and looked for the reference about solving...

I'm confused with the definition of the expectation operator. Assume a random variable $X$ having a probability distribution $p(x)$. Then the expecte...

What is the chance of rolling doubles in three six sided dice? The answer I have is: $$ \frac{1}{6}•\frac{1}{6}•\frac{3}{2} = \frac{1}{24} $$