College calculus solver
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Solution
Understand the method, then try it yourself
Explore calculus with attention to domains, substitution, and interpretation. This page is for college-level practice where an answer may need a justification as well as a calculation. Include bounds and assumptions, and ask which theorem supports the argument.
Worked example
Evaluate the integral of 2x cos(x²) with respect to x.
- Choose u = x² because its derivative matches the factor 2x. Then du = 2x dx.
- Rewrite the integral as the integral of cos(u) du. Its antiderivative is sin(u) + C.
- Substitute back to get sin(x²) + C. Differentiate to check: the chain rule gives cos(x²) × 2x, matching the integrand.
Tips for a useful explanation
- Choose substitutions that simplify both the function and differential.
- Change bounds if you keep the new variable in a definite integral.
- Check an antiderivative by differentiating it.
Read the worked steps, check the result against the original question, and explain the method in your own words. If a step is unclear, include your attempt and ask about that step. AI can make mistakes; verify the reasoning and use the assistance your teacher permits.
Frequently asked questions
Should the constant of integration appear in a definite integral?
The final definite integral is a number, so no + C is needed. When evaluating with an antiderivative, the arbitrary constant cancels between the bounds.
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