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 Oct20 revised Specific form of differential equation deleted 2 characters in body Oct20 comment Specific form of differential equation I reworded my question. Hopefully its clearer now. Sorry if its still unclear. Oct20 revised Specific form of differential equation added 31 characters in body Oct20 asked Specific form of differential equation Oct16 awarded Popular Question Oct16 revised Quotient of two rational sequences and the nature of its limit added 19 characters in body Oct16 accepted Quotient of two rational sequences and the nature of its limit Oct15 revised Quotient of two rational sequences and the nature of its limit added 66 characters in body Oct15 revised Quotient of two rational sequences and the nature of its limit edited tags Oct15 asked Quotient of two rational sequences and the nature of its limit Oct15 answered Let$\ x$ be a real number between$\ 0$ and$\ 1$. Is it possible to write$\ e^{x}$ as a function of$\ \Gamma \left(x+1\right)$? Oct13 comment How do I choose between $\lim_{x\to a} \frac {f(x) - f(a)}{x-a}\$ and $\lim_{x\to a} \frac{f(a+h)-f(a)}{h}$? To avoid the symbolic "overkill" you could always write the short hand notation for the binomial expansion, e.g. $$(x+h)^4=\sum_{k=0}^4{4\choose k}x^{4-k}h^k,$$ especially for large powers. Oct12 comment Find the limit of a Riemann Sum $f (X)=(1-X)(1+X)$. Oct9 accepted Are these functions identical? Oct8 asked Is it possible to abstract a Riemann integral into a “higher” integral with measure? Oct8 answered How to calculate $\sum\limits_{k=0}^{n}{k\dbinom{n}{k}}$ Oct7 comment Calculating a complex definite improper integral: $I= \int_{0}^\infty x^{it}\,\mathrm{e}^{-ax}\, dx$ For a general treatment of these types of integrals, you may be interested in learning about the Bilateral Laplace Transform: en.wikipedia.org/wiki/… Oct3 comment how to calculuate $\int_0^ \pi \sqrt{1+x^2 \sin^2x}dx$ For what it's worth the integrand is symmetric, so we may write $$I = \frac{1}{2}\int_{-\pi}^\pi\sqrt{1+(x\sin x)^2}dx.$$ Oct2 reviewed Approve Algebraic Integers and Irreducible Polynomials Oct2 comment Change of variable in complex integral Your substitution should be $z=Re^{i\theta}$, so that $dz=Rie^{i\theta}d\theta$, and $0\leq \theta< \pi/4$. We make this substitution because the substitution describes the path $\Gamma$ which you give.