Exponential Integral Calculator
Free online exponential 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：指数积分 Ei(x) 在线计算器
Ei(x) = −∫₋ₓ^∞ e^(−t)/t dt（主值）， companion E₁(x) = ∫ₓ^∞ e^(−t)/t dt；x > 0 时 Ei(−x) = −E₁(x)。
指数衰减世界的"积分残骸"
E₁(1) = 0.2193839343955202736…；Ei(1) = 1.8951178163559367554…（别记混：小值是 E₁）
凡是"衰减核 × 幂律"的积分都落到 Ei/E₁：放射性衰变链的活度、恒星大气辐射转移、地下水中污染物穿透时间、电路里 RC 阶跃的精确解。Ei 在 x = 0 的对数奇点使它没法用普通数值积分硬算——本页在 x = 0 附近用 γ + ln|x| + 级数，大 x 用 eˣ/x 主导的渐近展开，两条路径在 x = 30 交接。
How to use the Exponential 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 Exponential 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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