Integral Calculator

Type sin, sqrt, ^, / naturally. Shorthand like sin3x works.
Preview type a function above…
Examples by method
Power rule
u-sub
By parts
Rational
Trig / log
Trig: sin(3*x) or shorthand sin3x.
x^2, sin(x), cos(x), tan(x), e^x, log(x)=ln(x), sqrt(x)
sec(x), csc(x), cot(x), sinh(x), cosh(x), tanh(x)
asin(x), acos(x), atan(x), pi, e, abs(x), 1/x
SymPy one-liner: integrand, (variable, a, b)
∫

Ready when you are

Type a function above and hit Integrate.

Integrate a function to see its graph.

Template:
Power rule ∫ xn dx = xn+1/(n+1) + C
u-substitution ∫ f(g(x))·g′(x) dx = ∫ f(u) du
By parts ∫ u dv = uv − ∫ v du

Frequently asked

Yes. Click the Print Worksheet button to open a bank of 1,000+ integration practice problems with full answer keys. Problems are organised by type (power rule, u-substitution, integration by parts, partial fractions, trig substitution, definite integrals) and four difficulty levels (basic, medium, hard, scholar). Filter, print, or work through them on screen — perfect for AP Calculus, college calculus, or self-study.
Indefinite integrals (antiderivatives) and definite integrals for polynomials, trigonometric functions (sin, cos, tan, sec, csc, cot), exponentials (e^x), logarithms (ln x), rational functions, hyperbolic functions (sinh, cosh, tanh), inverse trig (arctan, arcsin), and products solved by integration by parts. Handles power rule, u-substitution, and partial fractions.
Yes. After computing a result, click Show Steps to see a detailed step-by-step solution. For common integrals (power rule, basic trig, exponential), steps are generated instantly in your browser. For complex integrals like integration by parts or partial fractions, the advanced solver explains each algebraic manipulation, substitution, and simplification in 5–8 clear steps with full LaTeX math rendering.
Absolutely. The built-in worksheet has 1,000+ curated problems covering every integration topic on the AP Calculus AB/BC exam and standard college Calculus II courses: power rule, u-substitution, integration by parts, partial fractions, trig substitution, improper integrals, and area/volume applications. Each problem includes a verified answer. Use the difficulty filter to ramp from easy to exam-level.
Yes — four ways: (1) Download PDF with the question, answer, method, and step-by-step solution beautifully formatted, (2) Copy LaTeX for papers and documents, (3) Copy Text for plain email/chat, or (4) Share to generate a URL that re-loads your exact integral with one click.
An indefinite integral finds the antiderivative F(x) + C — a family of functions whose derivative equals f(x). A definite integral evaluates the net signed area under the curve between bounds [a, b] using the Fundamental Theorem of Calculus: F(b) − F(a). This calculator supports both modes via a simple toggle; the interactive graph shades the area for definite integrals.
Completely free with no signup, no account, and no limits. You get symbolic integration, step-by-step solutions, interactive graphs, PDF download, LaTeX export, a 1,000+ problem worksheet, and a built-in Python compiler. All computation runs in your browser for instant results.
U-substitution (change of variables) rewrites ∫ f(g(x))·g′(x) dx as ∫ f(u) du by letting u = g(x). The calculator auto-detects when u-sub applies and shows the substitution step. Example: ∫ 2x·cos(x²) dx becomes ∫ cos(u) du with u = x². Click Show Steps to see the full u-sub workflow.