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Aug
9
revised Inequality relating harmonic numbers
added 288 characters in body
Aug
9
answered Inequality relating harmonic numbers
Aug
9
comment $n\text{ odd}\implies n^2=8k+1$ for some $k\in \mathbb{Z}$
In looking at number theory problems, fractions can lead to error. It is preferable to keep things "flat," and work with $4m^2+4m+1=4(m^2+m)+1$. Now one of $m$ or $m+1$ is even, so you are finished. Alternately, whether $m$ is even or odd, $m^2+m$ is even.
Aug
9
comment Integrate $\int{\frac{\sin(2x)+\cos(2x)}{(\sin(2x)-\cos(2x))^{5/2}}}\ dx$
You posted an erlier problem that was structurally almost the same as this one. It is important to use MSE answers to solve problems on your own.
Aug
9
revised Find density functions from two dimensional function
added 289 characters in body
Aug
9
answered Find density functions from two dimensional function
Aug
9
comment Integrate $\int x^2(8x^3+27)^{2/3}\,dx$
Very nice answer, goes forward from what OP did.
Aug
9
comment Integrate $\int x^2(8x^3+27)^{2/3}\,dx$
Your idea of $u=8x^3$ is an OK first step, but we might as well throw in the $27$, it won't change $du$.
Aug
9
answered Integrate $\int\frac{\sin x+\cos x }{(\sin x-\cos x)^{1/3}}dx$
Aug
9
answered How do I show that $\gcd(a^2, b^2) = 1$ when $\gcd(a,b)=1$?
Aug
8
comment Problem involving Properties of continuous functions
It was just protection against the $\le$ changing to $\lt$, the posted question changed a few times.
Aug
8
comment For a joint distribution probability $X>Y$
You have written down the integral for $\Pr(X\lt Y)$. Note that you have $x$ going up to $y$.
Aug
8
comment Symmetry functions and integration
For a formal proof of the first result, break up the integral as $\int_{-a}^0f(x)\,dx+\int_0^a f(x)\,dx$. For first integral, make substitution $u=-x$.
Aug
8
comment Symmetry functions and integration
Examples of even functions: $x^4-3x^2+17$, $e^{-x^2}$, $e^{x}+e^{-x}$, $\cos x$, $\sin^2 x$; Examples of odd functions: $x^3-5x$, $\sin x$.
Aug
8
revised Problem involving Properties of continuous functions
deleted 396 characters in body
Aug
8
answered Problem involving Properties of continuous functions
Aug
8
revised Using the Legendre Symbol
added 42 characters in body
Aug
8
comment Choice of at least one tutorial group in this Probability question
Yes, very nice explanation of the process.
Aug
8
revised Simple question about antiderivative?
added 129 characters in body
Aug
8
comment Using the Legendre Symbol
Soon you will hope for a Legendre symbol calculation on a test! The point is that there is a mechanical and relatively quick algorithm for determining whether $a$ is a QR of $p$ or an NR of $p$.