Can you help me with solving this integral $$\int \cosh^4(7x) \, dx \text{ ?}$$ I tried use subs but i got $$\cosh^4(t)=m$$ $$t = \pm\operatorname{arccosh...

I have the following series : $$\sum_{k=1}^{\infty }\left ( \frac{k}{\sqrt{4k^{3}+1}} \right )$$ And I am trying to see if it's convergent or diverge...

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This is a follow up to my earlier question "Understanding Higher Dimensional Solution Set". The answer to that question determined that the solution set o...

I'm supposed to compute the asymptotic density of the set \begin{equation} \Pi(x):=\#\{p^k \leq x :p \;prime, k \in \mathbb{N}\} \end{equation} of pr...

I'm reading some Linear algebra notes I found online, and am a bit confused about the following: If $U,V$ are finite dimensional $\mathbb{C}$-spaces ...

Find the area enclosed by $y=x$, $y=3x$ and $y=4-x$. Looking at the graph, $$A = \int_0^2 (3x)-(4-x)\, dx - \int_{0}^2 x\, dx=-2$$ Clearly the area is abo...

Let $ABC$ be a triangle. Let the external bisector of angle $A$ meet the circumcircle of triangle $ABC$ again at $M \neq A$. A circle with centre $M$ and ...

I am reading the book of characteristic classes by Milnor-Stasheff, and I have a problem with the exercise 4-A: Show that the Stiefel-Whitney classes of a...

For a class assignment I need to calculate the probability of winning the game called Casino War. I've never done anything with chance before (only h...