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Integrating Exp & Log Online Calculator

Exponential/logarithm integral calculator. Enter an expression and interval to integrate numerically, supporting by-parts and substitution—for technique drills.

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∫ ln x dx = x ln x − x + C
Supports + - * / ^ ( ) and sin cos tan sec cot sqrt exp log abs asin atan pi e; write 2*x, not 2x
Lower limit of integration
Upper limit of integration

📖 Tutorial | Integrating Exp & Log

1. Definition
∫eˣ dx=eˣ+C; ∫aˣ dx=aˣ/ln a+C. Logarithms use parts: ∫ln x dx=x ln x−x+C. Products of e^x with x, or ln with polynomials, often use parts/substitution.
2. Common formulas
SymbolsMeaning
∫eˣeˣ+C
∫aˣaˣ/ln a+C
∫ln xx ln x−x+C
∫1/xln|x|+C
∫x eˣ(x−1)eˣ+C
3. How it works
  • Adaptive Simpson integrates exp/log expressions directly;
  • It verifies by-parts or substitution results;
  • ln requires x>0.
4. Steps
  1. Enter an expression, e.g. exp(x) or log(x);
  2. Enter [a,b] (keep it positive for ln);
  3. Click Calculate for the numeric integral.
5. Example
Example: ∫₀¹ eˣ dx = e−1 ≈ 1.718282. Also ∫₁^e ln x dx = 1. Tool: 1.000000.
6. Pitfalls
The argument of ln must be positive;
log means natural logarithm here;
Products like x eˣ, x ln x use by parts.

❓ FAQ | Integrating Exp & Log

Is log base-10 or natural?
Here log is the natural logarithm ln(x).
How to integrate ln x?
Treat it as 1·ln x with u=ln x, dv=dx; result x ln x−x.
Can e^(x^2) be integrated?
It has no elementary antiderivative; only a numeric value is possible.
Why does log(0) fail?
ln is defined only for x>0.
Notation?
exp(x), log(x), e, pi and common operations.