Integral Calculator

Calculate the indefinite integral (antiderivative +C) or definite integral (with bounds a and b) of common function types. Shows the integration formula and the numerical result.

Function Type

n (exponent)

Integration Formulas

Power Rule: ∫axⁿ dx = a·xⁿ⁺¹/(n+1) + C (n ≠ −1)

Sine: ∫a·sin(bx) dx = −(a/b)·cos(bx) + C

Cosine: ∫a·cos(bx) dx = (a/b)·sin(bx) + C

Exponential: ∫a·e^(bx) dx = (a/b)·e^(bx) + C

Log: ∫a·ln(x) dx = a·x·(ln(x) − 1) + C

'What does + C mean in integration?', 'answer' => 'The + C represents the constant of integration. Because the derivative of any constant is zero, there are infinitely many antiderivatives differing only by a constant. In definite integrals, C cancels out.'], ]" />

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