Indefinite Integration - 28 Problem types that can come in IIT JEE - JEE Main 2025

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Indefinite Integration is one very big topic in Mathematics. Making this video of indefinite integrals took tremendous amount of effort to build up as well. We are going to systematically start with weightage of the topics in JEE Main and then we are going to systematically move towards the syllabus comparison from 2023_24 to 2025.

Then we are going to see what are the exact details of the Syllabus using a mind map and then we'll go into 28 problem type categories in which I have classified all the last 5 to 10 years of questions that came in JEE Main.

In order to make this chapter super simple, we have started this video with weightage of Indefinite Integration in JEE and then we systematically go into the syllabus comparison between JEE Main 2024 and JEE Main 2025. This will ensure you have an exact idea of the differences.

Then we will jump into the Mind map of the chapter, so you know which topics and subtopics are covered in Indefinite Integration chapter for IIT JEE - JEE Main and JEE Advanced, and how these are interlinked with each other. That helps you cover the entire Indefinite Integration chapter comprehensively and ensure you do not miss any single subtopic or concept from it.

Since the video has 5-6 questions from each of the 13 types of problems in Indefinite Integration, mostly from Past Year Questions of JEE Main, we are keeping 2 questions per type in the blog. We will add the list of the 28 problem types followed by 2 questions from each type.

We are going to systematically start with the weightage of the topic then go into the subtopics that need to be covered then go into more deeper points of what exactly there is in the syllabus using mind maps and ultimately come on to the 28 problem types that can be asked in Indefinite Integration chapter.

Before we start this video there is a “do” and there is a “don't”. The “do” is do not watch this video like you are watching a movie but keep making notes, keep solving questions, pause the video and see how you can arrive on an answer and develop your approach while solving. The “don't” is that this video is not meant for a fresher student who has not just done Indefinite Integration. We will not go into very Basics but yes, I will tell you the concept wherever and whenever it is required.

So, without any further delay let us start with the weightage of Indefinite Integration. It is 1 question in every JEE Main paper. It may differ from attempt to attempt. Actually, we should understand the syllabus more or weightage more in terms of integral calculus. Integral calculation will have five questions from it largely one and two questions will come from area and differential equations and then three questions will come from indefinite and definite. Usually, students think that from indefinite not many questions are asked but the reality is that those questions get asked indefinite integrals to definite integrals form.

They will ask questions in which you have just limits over that indefinite question and you will have to use the same technique as you solve an indefinite integral question. So, let us understand that the integration part will have three questions as weightage and this is the part of that larger integration chapter.

If I look into the syllabus comparison, you see nothing has changed in the syllabus and it remains the same compared to last 2 years.

Mindmap of the chapter – Indefinite Integration

More interesting enough in mind map you can see that we'll start with the meaning of indefinite integration, then we move towards technique of splitting an indefinite integral into two such integral which are in standard forms and can be integrated to get an answer when we move towards the idea of substitution and we look into standard substitution. Then using that we find 1 by quadratic and 1 by root of quadratic kind of questions, invisible second term regeneration, important formulas, reduction formula and ultimately, we move towards questions based on partial fraction where we solve five problem types and then we slowly move towards trigonometry where we solve nine problem types. Then we move towards rational functions where we solve three problem types and in irrational function, we take care of five problem types in this manner for JEE Mains point of view.

In the standard note there are 35 problem types but usually what I have seen in JEE Mains that not more than 20 have been asked. I presume that there are more eight problem types that can be asked so that eight also we have included in the process of making this video. So, this is an exhaustive video. After watching this video, I don't think you will require any more problem types to solve problems based on indefinite integrals.

Largely in order to understand this chapter it is a very good idea to understand in terms of algebra of integrals. Yes, there is nothing like algebra of integrals. We have learned algebra of differentiation so in order to compensate that integrals have come up with some techniques so what I'm trying to tell you is like when we have sum of two integrals or sum of two functions in case of differentiation we can distribute that over it so if you have X Plus sin x you can differentiate X and then you can add and differentiate the sin(x) part but in this case also if you have X and sin(x) we can still distribute the integral sign over it the second is basically if you have been given a composite function.

Now in case of differentiation for composite function you have something known as chain rule. Instead of chain rule what we are using here is a technique of substitution for functions into multiplication. You have a product rule in differentiation, instead of product rule what we have here is nothing but the bi parts and for division of functions what we had was a quotient rule but instead of quotient root what we have here is partial fractions. Here you can see that we are doing exactly the same thing but instead of using algebra we are using these three very important techniques.

In fact, with these four very important techniques what we will do is that every question when we are solving, either we are going to split it into two known integrals, either we are going to apply some kind of substitution or we will apply bi parts or partial fraction to solve the question. So, inherently in this chapter there are only these four techniques that needs to be applied while solving a question.

Now let us move into the first idea that is algebra of integrals and where we will use the idea of splitting an integral into two integrals in the form of addition and subtraction of two integrals and we'll solve the question. This is the first important idea - To take an integral and split it into two standard integrals, apply the formula and get the answer. Now we are not taking some specific problems on this idea because this idea will be inherent in all the problem types you will find in all the problem types when you move forward. It is an underlying theme that will always be there.

The next idea is nothing but substitution. As we know substitution is applicable for composite functions and there is this process of doing it so we will not go into the details of it. Basics you all know this is the process that we are going to use so now there are two things when you're looking into a composite function like this. So, there are two ways to look into it - one is either you look for the composite function or you look for the derivative of g(X).

It is very important to understand whose composite function it is and then put that substitution so in order to understand what substitution to put you'll have to either look for from where this composite function is getting generated or what is the derivative so we'll observe g of X, figure out F of g(X) put g(X) = to T, differentiate replacing g(X) by g(T) and d(X) by d(T). By this the integration will reduce into some kind of a standard integral, we'll apply the formula and we'll get the answer. The interesting thing here is don't forget the constant of integration. In Objective questions it does not matter because they will give you the constant of integration.

Indefinite Integration /Integrals Revision Notes

We now move to some concise theory of the chapter Indefinite Integration. It can serve as notes as well as revision tool. These notes are mostly sufficient for you to comprehensively revise the chapter and then proceed on to the questions. After that we will move to the 28 problem types in Indefinite Integration with examples.

“In Differentiation we had formulas but in Integration we will have techniques.”

Algebra of Integrals-Add/Sub
Algebra of Integral

Substitution

Algebra of Integrals

•Composition

•Substitution

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