An integral calculator with steps solves indefinite integrals (antiderivatives) and definite integrals (areas under curves) and shows every step of the work. It’s one of the most useful tools for calculus students, because seeing which technique to use, and why, is the hardest part of integration.
Start with the basic rules. The power rule says ∫xⁿ dx = xⁿ⁺¹ ÷ (n + 1) + C, for n ≠ −1. So ∫(3x² + 4x) dx = x³ + 2x² + C. For definite integrals, evaluate the antiderivative at the upper and lower limits and subtract: ∫₀² 3x² dx = [x³]₀² = 8.
Common techniques: u-substitution reverses the chain rule. For ∫2x cos(x²) dx, let u = x², du = 2x dx, so the integral becomes ∫cos(u) du = sin(x²) + C. Integration by parts, ∫u dv = uv − ∫v du, handles products like ∫x eˣ dx = x eˣ − eˣ + C. Partial fractions break rational functions into simpler pieces, and trig substitution handles expressions like √(a² − x²).
Common mistakes: forgetting the + C on indefinite integrals, not changing the limits when using substitution in a definite integral, and sign errors with trig functions. Always check your answer by differentiating it; you should get back the original function.
Why use an online Integral Calculator with Steps: it saves time, avoids simple arithmetic mistakes and shows each step, so you can check your homework, plan a project or make a decision with confidence. Bookmark the page so it’s ready the next time you need it.
Tips for getting accurate results from the Integral Calculator with Steps: double-check that every input uses the right units, enter numbers without commas or symbols, and run the calculation a second time with a quick estimate in your head to confirm the answer looks reasonable.
Learn more on Wikipedia’s integral article. Find double integral, Simpson’s rule and Laplace transform calculators on Minedit.