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odenut6b 2022-09-27

Evaluating ${\int }_{0}^{\frac{\pi }{2}}{\left(\frac{1}{\mathrm{log}\left(\mathrm{tan}x\right)}+\frac{1}{1-\mathrm{tan}\left(x\right)}\right)}^{3}dx$Using the method shown here, I have found the following closed form.${\int }_{0}^{\phantom{\rule{negativethinmathspace}{0ex}}\frac{\pi }{2}}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{negativethinmathspace}{0ex}}{\left(\frac{1}{\mathrm{log}\left(\mathrm{tan}x\right)}+\frac{1}{1-\mathrm{tan}x}\right)}^{2}\phantom{\rule{negativethinmathspace}{0ex}}\mathrm{d}x=3\mathrm{ln}2-\frac{4}{\pi }G-\frac{1}{2},$where $G$ is Catalan's constant.I can see that replicating the techniques for the following integral could be rather lenghty.${\int }_{0}^{\phantom{\rule{negativethinmathspace}{0ex}}\frac{\pi }{2}}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{negativethinmathspace}{0ex}}{\left(\frac{1}{\mathrm{log}\left(\mathrm{tan}x\right)}+\frac{1}{1-\mathrm{tan}x}\right)}^{3}\phantom{\rule{negativethinmathspace}{0ex}}\mathrm{d}x$My question: Could someone have, ideally, a different idea to evaluate the latter integral?

Chelsea Lamb 2022-09-27

Does the logarithm inequality extend to the complex plane?For estimates, the inequality $\mathrm{log}\left(y\right)\le y-1,$$y>0$ is often helpful. Is there any sort of upper bound for the logarithm function in the complex plane? Specifically, $|\mathrm{log}\left(z\right)|\le$ something for all $z\in \mathbb{C}$Perhaps this would work?: $\mathrm{log}\left(z\right)\le \sqrt{{\mathrm{log}}^{2}|z|+\mathrm{arg}\left(z{\right)}^{2}}$

traffig75 2022-09-27

One ounce is equal to 28.35 grams. convert 16 ounces to grams round your answe to the nearest tenth

Lustyku8 2022-09-26

I tried plotting the step and impulse responses in Matlab:sys = tf([1 0],[1 -0.5])figure(1);step(sys);figure(2);impulse(sys);However, both graphs look the same (can't post images of my graphs, I need more rep to do it).Both graphs have exponential growth, but shouldn't the impulse response look like exponential decay?

Haiphongum 2022-09-26

Logarithmic equationI'm studying logarithms and I encountered this equation:$\left[{\mathrm{log}}_{9}\left(k+1\right){\right]}^{2}+{\mathrm{log}}_{9}\left(k+1\right)+\left(k+1\right)>3$I tried a lot but I still couldn't solve it! I know this may be easy for most of you but please could you help me?Thanks!

Stacy Barr 2022-09-26

Perimeter =48 mLet the length be 𝑥 m and the breadth be 𝑦 mAs we know, Perimeter =2(𝑥+𝑦)=48 $⇒x+y=24$ 𝑥+𝑦=24 [⋯(1)]Area=135 m${}^{2}$.As we know, Area=𝑙𝑏Therefore, 135 m${}^{2}$ =𝑥𝑦 [⋯(2)]

fion74185296322 2022-09-26

Proving a local minimum is a global minimum.Let $f\left(x,y\right)=xy+\frac{50}{x}+\frac{20}{y}$, Find the global minimum / maximum of the function for $x>0,y>0$Clearly the function has no global maximum since $f$ is not bounded. I have found that the point $\left(5,2\right)$ is a local minimum of $f$. It seems pretty obvious that this point is a global minimum, but I'm struggling with a formal proof.

Megan Herman 2022-09-26

If the area of the rectangle below in 4 square feet, what is the value of x?$\frac{1}{3}$$3x-6$1) 32) 63) 94) 12

koraby2bc 2022-09-26

How do you use linear models to make pblackictions?

Joyce Sharp 2022-09-26

Fractions with sum 1Using all numbers 0 to 9 only once, form two fractions whose sum is 1.I have tried every possible combination but with no luck. I believe the fractions must be xx/xx + xxx/xxx but I am not sure. Any ideas are most welcome. I even tried getting all different ways to select 3 out of 10 digits, then omitting all the primes and trying to make fractions with simple values 1/3, 1/4, 2/5 etc using only different digits but again with no luck! By the way, two years ago I was given a similar one, with three fractions and without the digit 0, for which I found a solution 7/68+9/12+5/34 but now I am stuck!!

basaltico00 2022-09-26

Fint 30th term of the arithmetic series 2, 5, 8, …

wijii4 2022-09-26

Find the 30th term of the arithmetic series 2, 5, 8, …

trkalo84 2022-09-26

Find the slope of a line perpendicular to the line whose equation is 5x+3y=8

Camila Brandt 2022-09-26