∫Integral Calculator

Compute indefinite and definite integrals with step-by-step solutions.

Enter Integrand
∫ dx
Type:
Variable: Use ^ for powers, * for multiply
Steps: Full working
Try these examples
$x^3 + 2*x - 5$$sin(x)$$cos(2*x)$$exp(x)$$1/x$$x*exp(x)$$x*sin(x)$$x*ln(x)$$sqrt(x)$$x^2 + sin(x)$$arctan(x)$$sin(3*x + 2)$
Steps Modes
None  Clean answer only.
Summary  Pill list of every rule used.
Detailed  Accordion: before → after expressions, formula & explanation per step.
Definite mode evaluates F(b) − F(a) numerically.
Integration Rules
Constant$∫c dx = cx$
Power$∫xⁿ dx = xⁿ⁺¹/(n+1)$
Reciprocal$∫1/x dx = ln|x|$
Sum$∫(f±g) = ∫f ± ∫g$
Const ×$∫cf = c∫f$
∫sin(x)$−cos(x)$
∫cos(x)$sin(x)$
∫tan(x)$−ln|cos(x)|$
∫eˣ$eˣ$
∫ln(x)$x·ln(x)−x$
∫aˣ$aˣ/ln(a)$
∫arctan(x)$x·arctan(x)−½ln(1+x²)$
Supported Functions
sin()cos()tan()cot()sec()csc()arcsin()arccos()arctan()sinh()cosh()tanh()ln()log()sqrt()exp()abs()
Linear substitution auto-applied for f(ax+b) patterns.
Input Tips
  • x^2 → x²
  • x^(-1) → 1/x
  • exp(x) → eˣ
  • sin(3*x+2) → sin(3x+2)
  • sqrt(x) → √x
  • 2.71828 → e
  • Bounds: use 3.14159 for π
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