Math Queue

$$ \text{Improper integrals with bounds 0 to infinity} $$

$$ \text{Proving} \left(1-\frac13+\frac15-\frac17+\cdots\right)^2=\frac38\left(\frac1{1^2}+\frac1{2^2}+\frac1{3^2}+\frac1{4^2}+\cdots\right) $$

$$ \frac {\zeta(2)}{e^2} + \frac {\zeta(3)}{e^3} + \frac {\zeta(4)}{e^4} + \frac {\zeta(5)}{e^5}.....? $$

$$ \int_0^{\frac\pi{2}}\frac {\cos\left((1-2n)\arcsin\left(\frac{\sin(\theta)}{\sqrt 2}\right)\right)}{\sqrt{1-\frac{\sin^2 \theta}{2}}}d\theta $$

$$ \text{General solution to }\int \frac{1}{x^n +1}dx \text{ where } n \text{is an integer?} $$

$$ \text{Trying to prove } \left(1-\frac13+\frac15-\frac17+\cdots\right)^2=\frac38\left(\frac1{1^2}+\frac1{2^2}+\frac1{3^2}+\frac1{4^2}+\cdots\right) $$

$$ \text{In an attempt to find } I = \int_0^\infty \frac{t}{e^t-1}dt $$

$$ \text{Representing the cyclic differentiation pattern of } \frac{d^n}{dx^n}(\sin(x)) \text{ using linear algebra.} $$

$$\text{Trigonometric terms for floor function } Q_k(n)$$

$$ \text{The harmonic Series sequence.} $$

\[ \int_0^1 \frac{e^{-x^2(t^2+1)}}{t^2+1}\,dt, \text{ find } g'(x) \]

$$ \text{Which of the two quantities } \sin 28^{\circ} \text{and} \tan 21^{\circ} \text{is bigger.} $$

$$I = \int_{0}^{\infty} \frac{x}{\sqrt{e^{2\pi\sqrt{x}}-1}}\,dx$$.

$$ g(x) = \int_0^1 \frac{e^{-x^2(t^2+1)}}{t^2+1} \, dt \text{ find } g'(x). $$

$$ \text{Sum of Squares of Harmonic Numbers} $$

Testing-purpose

$$ \int \frac{1}{x^n +1}dx \text{ where } x \in \mathbb{R} \text{ and } n \in \mathbb{Z} $$

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