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Integration by parts, Taught not just answered. 

A real-time, 1:1 lesson on Integration by parts: an AI teacher explains it out loud while it visualizes every step. Interrupt it, ask why, and it checks you got it, in 26 languages.

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The idea

What is Integration by parts?

Integration by parts is a technique for integrating a product of two functions, derived by reversing the product rule for derivatives. If you split the integrand into one piece u that becomes simpler when differentiated and another piece dv that you can integrate, the formula says the integral of u dv equals uv minus the integral of v du.

Where it appears: Class 12 CBSE, A-level Further Maths, IB Mathematics AA HL, AP Calculus BC, JEE, first-year university.

Where learners get stuck

Why Integration by parts is hard

Choosing which factor is u is the whole game, and learners pick wrongly so the new integral is harder than the first; integrals like x times e to the x versus ln x confuse the choice.

The picture a good explanation starts with: The product rule written out, then rearranged with integral signs on both sides so the by-parts formula appears, with u and dv boxed in colour.

A lesson, step by step

How a lesson on Integration by parts goes

  1. 01

    Ask

    Type or say "How do I decide which part to call u?" in your own words, in any of 26 languages.

  2. 02

    Plan

    The tutor plans a storyboard, one picture per idea, starting with the product rule written out, then rearranged with integral signs on both sides so the by-parts formula appears, with u and dv boxed in colour.

  3. 03

    Explain

    It explains Integration by parts out loud while the picture builds step by step, pitched to your level (Class 12 CBSE and up).

  4. 04

    Interrupt

    Say "wait, why?" or type a doubt: it stops, answers over the picture, and carries on. Ask for a different explanation any time.

  5. 05

    Check

    A checkpoint question makes sure the idea landed, and Test Lab keeps the practice going.

  6. 06

    Your notes

    Upload a PDF or a photo of your class notes or a past paper and the lesson follows your textbook's terms.

Ask it anything

Questions learners ask about Integration by parts

  • How do I decide which part to call u?
  • Why does integrating ln x need integration by parts?
  • What happens when the original integral shows up again?

Any of these, or your own, typed or spoken. The tutor answers on the picture and adapts to how well you are following.

Questions

Asked, Answered

Can LetMeTeach explain Integration by parts?

Yes. Ask in your own words and the tutor plans a lesson on Integration by parts: it starts with the product rule written out, then rearranged with integral signs on both sides so the by-parts formula appears, with u and dv boxed in colour. Then it explains each step out loud as the picture builds, stops when you say "wait, why?", and ends with a checkpoint question.

Where does Integration by parts come up?

Class 12 CBSE, A-level Further Maths, IB Mathematics AA HL, AP Calculus BC, JEE, first-year university. The lesson is pitched to your level and the exam or curriculum you follow, and you can upload your own notes or past papers so it uses your textbook's terms.

Can I learn Integration by parts in my own language?

Yes. LetMeTeach teaches in 26 languages and plans the lesson in the language you choose rather than translating an English one, so the terms match what your textbook says. The Free plan includes 7 hours a month with no card.

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Learn Integration by parts, Starting now.

Ask "How do I decide which part to call u?" and watch the answer drawn. The Free plan needs no card.

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How it works