Example 1
Integrate (3x^2 - 4x + 1) dxA polynomial antiderivative with the constant of integration.
Integral Solver
Purpose-built solver page
Integral Solver
Use this integral solver for worked help with indefinite and definite integrals. Ask for a method such as substitution, integration by parts, or partial fractions when you want that technique explained.
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∫ f(x) dx
Indefinite integrals
Definite integrals
Substitution and parts
integral solver
Solve your integral problem
Enter your integral problem below. Add the variable, conditions, and method you want so the AI can return a more relevant worked response.
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∫ f(x) dx
What this Integral solver is designed for
The page is organized around the problem types people actually search for, while staying within the text-and-image solver's current capabilities.
∫ₐᵇ f(x) dx
Indefinite integrals
∫ f(x) dx = F(x) + CFind a family of antiderivatives and retain the constant of integration.
Definite integrals
∫ₐᵇ f(x) dx = F(b) − F(a)Evaluate an antiderivative at the given bounds and interpret the signed result.
Substitution and parts
u = g(x)Recognize composite structure or a useful product split before applying a technique.
Rational integrands
∫ u dv = uv − ∫ v duSimplify, divide, or decompose into partial fractions before integrating.
Step
How to use the Integral solver
A complete prompt usually produces a more useful explanation than an isolated expression.
- 1
Enter the integrand
f(x) dxUse parentheses clearly and specify the integration variable.
- 2
Include bounds
[a,b]For a definite integral, give both the lower and upper limits.
- 3
Choose and review a method
u / dvCheck the substitution, parts selection, identity, or decomposition used.
- 4
Verify
d/dx [F(x)]Differentiate an indefinite result or estimate the sign and size of a definite integral.
Tip: ask for a named method, a domain, or a verification step when your course requires one.
Example
Integral problems to try
These examples reflect common search intent and can be inserted into the solver as a starting point.
Example 2
Evaluate integral from 0 to 1 of x e^(x^2) dxA definite integral suited to substitution.
Example 3
Integrate x ln(x) dxA product that is naturally handled by integration by parts.
Common mistakes to watch for
A worked answer is most useful when you know which details are easy to lose along the way.
Forgetting +C
An indefinite integral represents a family of antiderivatives.
Dropping transformed bounds
When changing variables in a definite integral, either update the bounds or substitute back.
Choosing a method by appearance only
Check the derivative relationships in the integrand before committing to substitution or parts.
Integral solver FAQ
