Calculus solver step by step, with every rule explained
Calculus answers at the back of the book skip the part you need: which rule to use and why. Send a derivative, integral or limit (typed or as a photo) and your agent names each rule as it goes, checks the result by running Python, points out where your own attempt slipped, and leaves you one similar problem to try.
The prompt
- Solve this calculus problem step by step: [PROBLEM OR PHOTO]. My course is [COURSE], and we have covered [TOPICS COVERED SO FAR], so only use those methods. Here is my attempt: [MY WORKING]. Name the rule used in every step (chain rule, product rule, u-substitution, integration by parts, L'Hopital and so on) and say why it fits. Verify the final answer by running it in Python (differentiate my integral back, or check the limit numerically) and show me the check. If my attempt has a mistake, show the exact line. End with one similar problem and wait for my answer before showing its solution.
What to change
- [PROBLEM OR PHOTO]: Type it, e.g. "integral of x·e^(2x) dx", or attach a photo of the problem and say which number.
- [COURSE]: E.g. "Calculus I", "AP Calculus BC", "A-level Further Maths", "first-year engineering".
- [TOPICS COVERED SO FAR]: E.g. "derivatives and u-substitution, not integration by parts yet". Keeps the method at your level.
- [MY WORKING]: Type your steps or attach a photo. Write "none yet" if you are stuck at the start.
Example result
- Problem: find the integral of x·e^(2x) dx
- Course: Calculus II. Method allowed: integration by parts.
- Why integration by parts
- The integrand is a product of a polynomial (x) and an exponential (e^(2x)). Differentiating x makes it simpler, and e^(2x) is easy to integrate, so the LIATE order says: u = x, dv = e^(2x) dx.
- Step by step
- • Step 1: pick u and dv. u = x, so du = dx. dv = e^(2x) dx, so v = (1/2)e^(2x).
- • Step 2: apply the formula. The integral of u dv = uv − the integral of v du.
- • Step 3: substitute. = (x/2)e^(2x) − the integral of (1/2)e^(2x) dx
- • Step 4: finish the last integral. The integral of (1/2)e^(2x) dx = (1/4)e^(2x)
- • Answer: (x/2)e^(2x) − (1/4)e^(2x) + C, or (1/4)e^(2x)(2x − 1) + C
- Check (run in Python with SymPy)
- • diff((x/2)*exp(2*x) − exp(2*x)/4, x) returns x·exp(2x)
- • That is the original integrand, so the answer is correct.
- Your attempt
- You had (x/2)e^(2x) + (1/4)e^(2x) + C. Line 3 is the slip: the formula subtracts the second integral, so the sign of the 1/4 term must be minus. Differentiating your answer gives x·e^(2x) + e^(2x), which is one term too many.
- Remember
- • Always add + C on indefinite integrals.
- • Differentiate your answer to check it. It takes 30 seconds and catches sign errors.
- Your turn
- Find the integral of x·cos(3x) dx. Reply with your u, dv and final answer.
How to do it with todo.is
- Copy the prompt and fill in the problem, your course and what you have covered.
- Paste it into todo.is on the Today screen, or send it with a photo to your agent on WhatsApp or Telegram.
- Your agent replies with a step-by-step solution, a Python check and notes on your own attempt.
- Send your answer to the practice problem. Ask "show a different method" or "explain step 2 again" when something is unclear.
Tips for a better result
- Say which methods you have learned. A solution using a rule you have not met yet will not help on a test.
- For limits, ask the agent to also show a quick table of values near the point. It makes the idea click.
- Differentiate every integral you get back to the integrand. Your agent does this in Python, and you should learn to do it by hand.
- Ask for a graph (PNG) of the function and its derivative when a related rates or optimization problem feels abstract.
calculus solver step by step: FAQ
- Can it solve integrals and derivatives from a photo? Yes. Send a clear photo and say which problem you mean. If the notation is unclear, your agent repeats the problem back so you can confirm it.
- How does it check that the answer is right? It runs the problem in Python (SymPy) in its workspace: it differentiates integrals back, evaluates limits numerically, or plugs values into your answer, and shows you the result.
- Does it cover multivariable calculus and differential equations? Yes, including partial derivatives, double integrals and first-order ODEs. Tell it your course so the explanation fits the notation you use.
- Is using a calculus solver cheating? Using it to understand the method is like a tutor; copying answers for graded work usually is not allowed. Follow your school's AI policy and hand in work you did yourself.
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