Compute indefinite and definite integrals of polynomials using the power rule, with step-by-step work.
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Term 1
Term 2
Term 3
Bounds (optional, for definite integral)
Result
Step-by-step
Integrate f(x) = 3x^2 + 2x + 1
Apply the power rule term by term:
∫3x^2 dx = 1·x^3
∫2x^1 dx = 1·x^2
∫1x^0 dx = 1·x^1
F(x) = x^3 + x^2 + x + C
Also in Calculus
Calculus
An integral calculator applies the reverse power rule to find the antiderivative of polynomial functions. It handles both indefinite integrals (with + C) and definite integrals with upper and lower bounds.
For each term ax^n where n ≠ −1, the antiderivative is a/(n+1) · x^(n+1). When n = −1, the integral is a·ln|x|. Indefinite integrals include a constant of integration (+ C).
For definite integrals, evaluate F(b) − F(a) where F is the antiderivative and a, b are the bounds.
∫axⁿ dx = a/(n+1)·x^(n+1) + C
Power rule for integration (n ≠ −1).
Frequently asked questions
The constant of integration accounts for the fact that infinitely many functions share the same derivative. Any constant disappears when differentiated.
The power rule formula produces division by zero for n = −1, so the special case ∫x⁻¹ dx = ln|x| + C is used instead.
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