求解 log(sin(x)) | Microsoft Math Solver
The power series of \log(1 + x) converges only for -1 < x \leq 1 (notice the two different inequality signs). ... How do you calculate \displaystyle{f}'{\left({x}\right)} and use calculus to find the maximum value of \displaystyle{\sin{{\left({\ln{{x}}}\right)}}} on the interval [1, 10]?
不定积分计算器 : log(sin(x)) - 数字帝国
值在 x= 不定积分计算器 可以用分析整合的方法，计算出一个给定变量的函数的不定积分（原函数）。 它也可以画出函数和它的原函数的图像。
solve log (x) = sin (x) - Wolfram|Alpha
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Showing that $\\int_0^1 \\log(\\sin \\pi x)dx=-\\log2$
The function $\sin(\pi x)$ is symmetric with respect to $x=\frac{1}{2}$, hence $$\begin{eqnarray*}I=\int_{0}^{1}\log\sin(\pi x)\,dx&\stackrel{x\to 2z}{=}&2\int_{0}^{1/2}\left[\log(2)+\log\sin(\pi z)+\log\cos(\pi z)\right]\,dz\\&=&\log(2)+2I.\end{eqnarray*}\tag{3}$$
log (sinx) - Wolfram|Alpha
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Example 34 - Integration of log (sin x) from 0 to pi/2 - Teachoo
2024年12月16日 · Example 34 Evaluate ∫_0^(𝜋/2 ) logsin𝑥 𝑑𝑥 Let I1=∫_0^(𝜋/2 ) 𝑙𝑜𝑔(𝑠𝑖𝑛𝑥) 𝑑𝑥 ∴ I1=∫_0^(𝜋/2) 𝑠𝑖𝑛(𝜋/2−𝑥)𝑑𝑥 I1= ∫_0^(𝜋/2) 𝑙𝑜𝑔(cos𝑥 )𝑑𝑥 Adding (1) and (2) i.e. (1) + (2) I1+ I1=∫_0^(𝜋/2) 〖𝑙𝑜𝑔(sin𝑥 )𝑑𝑥+∫_0^(𝜋/2 ...
log(sin(x) - Wolfram|Alpha
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Graph natural log of sin(x) | Mathway
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Integral of $x\\log(\\sin x)$ - Mathematics Stack Exchange
$$ \int_{0}^{\pi/2}x\log\sin x\,dx = \int_{0}^{1}\frac{\arcsin(u)\log u}{\sqrt{1-u^2}}\,du\tag{1}$$ and by recalling $$ \arcsin(u) = \sum_{n\geq 0}\frac{\binom{2n}{n}}{4^n(2n+1)}u^{2n} \tag{2} $$ $$ \int_{0}^{1}\frac{u^{2n}\log(u)}{\sqrt{1-u^2}}\,du = \frac{\pi\binom{2n}{n}}{4^{n+1}}\left(H_{n-1/2}-H_n\right)\tag{3} $$ (where $(3)$ follows by ...
Compute the fourier coefficients, and series for $\\log(\\sin(x))$
2014年12月16日 · The goal is to compute the Fourier series of $g(x)=\log\sin x$ over $[0,\pi]$, or the Fourier series of $h(x)=\log\sin\frac{x}{2}$ over $[0,2\pi]$, or the Fourier series of $f(x)=\log\cos\frac{x}{2}$ over $[-\pi,\pi]$.
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