Logarithmic Integral Calculator
Free online logarithmic integral calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
中文版：对数积分 li(x) 在线计算器
对数积分 li(x) = ∫₀ˣ dt/ln t = Ei(ln x)——素数定理的主角：小于 x 的素数个数 π(x) ≈ li(x)。
素数计数的"最佳近似"
π(x) ~ li(x)（素数定理）；Riemann 改进版 R(x) = Σ μ(n)li(x^(1/n))/n 更贴真实计数
高斯 15 岁时盯着素数表猜出 π(x) ≈ li(x)，一个世纪后被哈达玛与德拉瓦莱-普桑证明（素数定理）。li 在 x = 1 有奇点、在 (1, x) 区间的积分取柯西主值；x < 1 时 ln t 为负，li 取负值。工程中 li 也出现在信号处理与统计的 score 函数里，但它的名声全部来自素数分布。
How to use the Logarithmic Integral Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Logarithmic Integral Calculator free?
Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.
Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-09-26
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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