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2d
awarded  Constituent
2d
awarded  Caucus
2d
answered Bound on and integral
Dec
19
comment Help with proposition whether it's true or false
Yes, the proposition is true or false. :)
Dec
19
answered Proving that $\int_0 ^1 \frac{\text{d}s}{\sqrt{1-s^2}}$ converges with no trig functions
Dec
19
comment Proving that $\int_0 ^1 \frac{\text{d}s}{\sqrt{1-s^2}}$ converges with no trig functions
@Venus Anyone who offers hyperbolic functions to someone asking for non-trigonometric functions is a dirty cheat! :)
Dec
19
comment Evaluate $\int_0^{\pi/2} \frac{\ln\left(e^{2x} + 1\right)}{1 + \sin2x}\mathrm dx$
@Integrator Work faster. Christmas depends upon you!
Dec
19
comment How to calculate the series?
But what if $|x|>1$?
Dec
19
comment Can this binomial summation be simplified?
@JLiu Since we're dealing with integer parameters, we can use the fundamental recurrence relations to prove this identity, and so reduce the hypergeometric function to a finite binomial sum.
Dec
19
comment How to integrate a fraction of the type $\frac{1}{(ax+b)^c(dx+e)^f}$?
In general, no. Wolfram alpha will return a hypergeometric function for the anti-derivative, but this is really just naming the integral as opposed to solving it.
Dec
19
comment The exact value of csc -420 degrees (Find the exact value of each trigonometric funtion)
FYI: when working in degrees, you can append a degree-symbol as a subscript by writing 420^\circ. E.g., $420^\circ$.
Dec
18
comment How to solve for $\theta$ in an expression involving linear and $\sin$ terms
The possibility of a Lambert-W solution to equations like this has occurred to me in the past, but I've failed every attempt to make it work. If this can be done I'd very much like to see it.
Dec
18
comment How to solve for $\theta$ in an expression involving linear and $\sin$ terms
You could begin by graphing expression to find an approximate value for $\theta$.
Dec
18
comment Calculating an integral with sine, cosine
The function you are trying to integrate is odd, so integrating over $\mathbb{R}$ will make the integral vanish to zero identically. Could there be a typo in the question statement?
Dec
18
revised Extending the result $\int_{0}^{\infty} \left( ( 1 - 2C(x))^{2} + (1-2S(x))^{2} \right) \, dx = \frac{4}{\pi} $
additional work
Dec
18
revised Extending the result $\int_{0}^{\infty} \left( ( 1 - 2C(x))^{2} + (1-2S(x))^{2} \right) \, dx = \frac{4}{\pi} $
Added more steps
Dec
18
answered Extending the result $\int_{0}^{\infty} \left( ( 1 - 2C(x))^{2} + (1-2S(x))^{2} \right) \, dx = \frac{4}{\pi} $
Dec
18
comment Prove two identities relating to series
@Roger209 The two problems are very much connected. Differentiating both sides of (1) will give you (2).
Dec
13
comment Evaluation of an improper integral
When in doubt, part it out!
Dec
13
comment Computing $\int \sqrt{1+4x^2} \, dx$
@rubik No, I almost always have to go back to the Wikipedia page and double check the formulas before I use them.