poirot
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 Apr 26 comment Anti-Derivative of $\ln(x^2 + 7)$ is kicking my butt, can anyone help? Investigate $\int \ln x$ first. Apr 18 comment Are all numbers expressible as a complex number? Not sure what you mean exactly, but there are the Quarternions $\mathbb{H}$ and the Octonions $\mathbb{O}$. Apr 3 comment Minimising the length of the vector $r(t) = \sqrt{2}\sin{t}\mathbf{i}+\cos{2t}\mathbf{j}$ for $t \in (0, \pi/2)$ Differentiate the magnitude, set to zero and solve. Second derivative may be required to decide min/max. Mar 31 comment Finding $\int \frac{e^x\left(-2x^2+12x-20\right)}{x^3-6x^2+12x-8}dx$ Partial fractions is the way to go. Yes it involves the $Ei(x)$ function, but the total sum of these terms cancels to zero, leaving the single term you require. Mar 31 comment Finding $\int \frac{e^x\left(-2x^2+12x-20\right)}{x^3-6x^2+12x-8}dx$ Maybe partial fractions? Or can the numerator be factorised? Mar 29 comment Why are mathematicians so interested in finding out the gaps between primes and the distribution (randomness) in primes? For interest/fun: the $n$-th prime number $p_n\sim n\log n$. Mar 25 comment Comparing infinite values In that case you don't deserve a downvote! Mar 25 comment Comparing infinite values This is not the whole expression under investigation (ps I did not downvote) Mar 20 comment Can a change of variable result in the evaluation of an integral in terms of elementary functions, whereas before the c.o.v. this was not possible? To clarify, the integral $I$, i.e. the primitive $F$ of $f$, is not elementary in the question. Mar 16 comment Find a succinct problem whose solution requires methods from many sub-branches of mathematics Check out this, particularly near the end. There are mentions of the different areas of Mathematics used in Wiles' proof: vimeo.com/18216532 Mar 15 comment Absolute value of complex number Assuming all other symbols are real numbers, it might help to first multiply top and bottom by the complex conjugate of the denominator, then expand the denominator. This will give you a complex number of the form $x+jy$, which you should then be able to find the modulus. Mar 6 comment How to do large number of arithmetic operations Try to be concise and efficient in the steps you take. Mar 3 comment Weird Inequality that seems to be true Afraid not: Try $x=2.5$ and $y=0.5$. Mar 2 comment How to calculate $\sum_{k=0}^{\infty}\int_k^{k+\frac{1}{2}} e^{-st} dt$ Try evaluating the integral, then summing, or take the sum inside the integral if you can, then evaluate, then integrate. Feb 25 comment Is this inequality for integrals correct: $\left|\int_{\mathbb{R}}\frac{f(x)}{g(x)}dx\right|>\left|\int_{\mathbb{R}}\frac{f(x)}{g(x)^2}dx\right|.$ Yes, thought so. Thanks for the counter-example :-) Feb 25 comment Is this inequality for integrals correct: $\left|\int_{\mathbb{R}}\frac{f(x)}{g(x)}dx\right|>\left|\int_{\mathbb{R}}\frac{f(x)}{g(x)^2}dx\right|.$ That seems to work after your edit, but the left integral is zero. Presumably I can construct similar examples where the left integral is non-zero. I'll try to construct one. Feb 25 comment Is this inequality for integrals correct: $\left|\int_{\mathbb{R}}\frac{f(x)}{g(x)}dx\right|>\left|\int_{\mathbb{R}}\frac{f(x)}{g(x)^2}dx\right|.$ Thanks for your answer. Not sure your counter-example works out though? I get $2>0.75$, which agrees with the inequality. Feb 24 comment Does $\mid x-y\mid>0,x\neq-y$ imply $\mid\mid x\mid-\mid y\mid\mid>0$? I think my answer would be correct for $x,y\in\mathbb{R}$, but as has been pointed out in the answers, my proof is incorrect for $x,y\in\mathbb{C}$. Feb 24 comment Does $\mid x-y\mid>0,x\neq-y$ imply $\mid\mid x\mid-\mid y\mid\mid>0$? Thanks, so my problem lies here: $x\neq y\implies |x|\neq |y|$ since complex $x,y$ on the same "complex circle" will have the same moduli. Feb 19 comment Integrate $I=\int_e^\infty\left(\frac{\log\log y}{y(y+1)}\right)^2dy$ using residue calculus? I actually meant from $1$, not $e$. My mistake.