Indefinite Integration - Problems Solving - 6 | Class 12th, JEE Mathematics | Rohit Ranjan (IIT KGP)

Описание: These two together teach decision-making, not just calculation — exactly what Class 12 students struggle with.

Indefinite Integration | Integration by Parts | Class 12 Maths

In this video, we solve a problem set based on Integration by Parts, focusing not only on solving integrals but also on how to choose the correct method in exams.

Two carefully selected problems are discussed to build clarity, strategy, and confidence for Class 12 CBSE board examinations.

🔹 Problem 1

Integrate
x · (log x)² dx

This problem is used to clearly explain:

How to select u and dv in integration by parts

Why logarithmic functions are preferred as u

Applying the ILATE rule logically (not mechanically)

Step-by-step evaluation using integration by parts

📌 Here, we take:
u = (log x)² and dv = x dx

🔹 Problem 2

Integrate
(x · eˣ) / (x + 1)² dx

In this problem:

Although integration by parts is possible, a smarter method is demonstrated

The identity
∫ eˣ (f′(x) + f(x)) dx = eˣ f(x) + C
is used to simplify the integration

Students learn how to recognize patterns involving eˣ in board exams

📌 This approach saves time and reduces calculation errors.

🔹 What you will learn in this video:

When and how to use integration by parts

Logical selection of u and dv

Identifying shortcuts using standard integration properties

Comparing multiple approaches and choosing the best one

Board-exam focused techniques and common mistakes

🔹 Why this video is important:
✔ Concept clarity over memorization
✔ Time-saving strategies for exams
✔ High-probability indefinite integration problems

This video is part of the Indefinite Integration playlist designed specially for Class 12 CBSE students.

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