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6h
awarded  Revival
9h
answered What is a $0\times0$ or $0\times3$ matrix?
22h
revised Express $C_n = \cosh(0) + \cosh(1) + \cosh (2) + \dots + \cosh(n)$
modified response to better reflect the stipulations of the problem
22h
answered Evaluation of $\int\frac{1}{x^2.(x^4+1)^{\frac{3}{4}}}dx$
23h
answered Express $C_n = \cosh(0) + \cosh(1) + \cosh (2) + \dots + \cosh(n)$
Apr
20
comment Integral of trig fraction using substitution?
The standard method of integrating rational functions of sines/cosines is the tangent half-angle substitution.
Apr
20
answered How to solve $\int \frac{(x-1)\sqrt{x^4+2x^3-x^2+2x+1}}{x^2(x+1)}dx$?
Apr
20
answered How to solve this integral by a simple way?
Apr
19
comment Show that the Wronskian of solutions of $y''+p(x)y'+q(x)y=0$ satisfies $\frac{dW}{dx}+pW=0$
You already calculated the derivative of the wronskian in terms of second derivatives of the two fundamental solutions. Use the original ODE to rewrite the 2nd derivatives.
Apr
13
comment Evaluation of Spence's function.
@KaziArafatAhmed The result of the integral is the dilogarithm by definition because the dilogarithm is defined as being the result of the integral. It's that simple.
Apr
13
comment Evaluation of Spence's function.
@ADG We could quibble over semantics, but I don't think there's anything wrong with saying $Li_2(z)$ is a closed form for the indefinite integral.
Apr
8
comment To whom do we owe this construction of angles and trigonometry?
Very sexy. Thanks for sharing!
Apr
8
comment How do I show $\int_{-\infty}^\infty \frac 1{(a^2+s^2)(b^2+s^2)} ds=\frac {\pi}{ab(a+b)}$ using the solution to the following Fourier transform?
Try partial fraction expanding the integrand.
Apr
8
accepted Solving 2nd order linear recurrence with non-constant coefficients
Apr
8
comment Calculate the lenght of $\vec{f}(t)=(\cos^4(t),\sin^4(t))$ from $0$ to $2\pi$
The term under the square root sign appears to be negative.
Apr
7
comment Convergence of double-infinite series
@HasanSaad Typically it represents $\mathbb{N}_0=\mathbb{N}\cup\{0\}$.
Apr
2
comment An indefinite integral
@Frank Where did you encounter this problem?
Apr
1
comment Integral $\int \frac{dx}{x^4+1}$
@john with teamwork, yes we can. :)
Apr
1
comment Does the following limit exist? (involving harmonic numbers)
For $k=n-1$, the second part of $d_{n,k}$ is a finite sum from $j=n$ to $j=n-1$. Can I presume that you are using the convention of assigning a zero value to such sums?
Apr
1
asked Solving 2nd order linear recurrence with non-constant coefficients