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Exponential Integral Calculator

Compute the exponential integral Ei(x) for any real x ≠ 0 to a chosen precision, using the convergent series γ + ln|x| + Σ xᵏ/(k·k!) or the asymptotic series for large arguments.

Related tools

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Double Integral CalculatorNumerically evaluate a double integral ∬ f(x,y) over a rectangular region.Improper Integral CalculatorEvaluate improper integrals with infinite bounds or discontinuities, with a convergence verdict.Line Integral CalculatorCompute scalar (∫ f ds) and vector (∫ F·dr) line integrals along a parametric curve in 2D or 3D.Surface Integral CalculatorCompute scalar (∬ f dS) and flux (∬ F·dS) surface integrals over a parametrized surface.Triple Integral CalculatorNumerically evaluate a triple integral ∭ f(x,y,z) over a rectangular box.Exponential Decay CalculatorSolve P(t) = P₀·e^(−rt) for any variable, with the half-life.Exponential Distribution CalculatorCompute exponential-distribution probabilities for waiting times from the rate λ, including P(X≤x), P(X>x) and a range.Exponential Equation SolverSolve exponential equations of six types — basic, coefficient, linear exponent, two bases, quadratic-in-a^x and shifted — with logarithms and a full step-by-step solution.

Exponential Integral Calculator works straight from this page — free, instant, nothing to install. You will find it under Calculus, with Double Integral Calculator and Improper Integral Calculator for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Exponential Integral Calculator do?

Compute the exponential integral Ei(x) for any real x ≠ 0 to a chosen precision, using the convergent series γ + ln|x| + Σ xᵏ/(k·k!) or the asymptotic series for large arguments.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

How is Exponential Integral Calculator different from Double Integral Calculator?

They sit next to each other but answer different questions: Double Integral Calculator is the one to open when you need it to numerically evaluate a double integral ∬ f(x,y) over a rectangular region. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Improper Integral Calculator is the closest one after this: Evaluate improper integrals with infinite bounds or discontinuities, with a convergence verdict.

What else is worth having open alongside it?

Line Integral Calculator and Surface Integral Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

All guides →
ExplainerHow Half-Life Works: What Is Left After 1, 3 and 10 Half-LivesOne half-life leaves 50%, three leave 12.5%, ten leave less than a tenth of a percent. The formula is a single line — the part worth understanding is why the answer never reaches zero.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.