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L-2 - Indefinite Integration

This document provides information about integration by parts, including examples of different types of integrals that can be evaluated using this method. It discusses 5 types of integrals where integration by parts can be used: 1) two separate functions are visible, 2) considering 1 as a function, 3) deja vu, 4) direct result 1, and 5) direct result 2. It also provides formulas and practice problems related to integration by parts. The document is presented by Sameer Chincholikar from IIT Roorkee as part of his online JEE preparation course.

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458 views74 pages

L-2 - Indefinite Integration

This document provides information about integration by parts, including examples of different types of integrals that can be evaluated using this method. It discusses 5 types of integrals where integration by parts can be used: 1) two separate functions are visible, 2) considering 1 as a function, 3) deja vu, 4) direct result 1, and 5) direct result 2. It also provides formulas and practice problems related to integration by parts. The document is presented by Sameer Chincholikar from IIT Roorkee as part of his online JEE preparation course.

Uploaded by

MOKSH AGARWAL
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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12

CLASS

Indefinite
Integration
Integration By Parts
( & D.I. Method)

SAMEER CHINCHOLIKAR
Sameer Chincholikar
IIT Roorkee
12+ Years of Teaching Experience
Trained Million+ students
Author - Top Ranker’s Series (TRS)
Bratin Mondal Amaiya Singhal

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Integration By Parts
Integration by parts:

(First function) into (integration of second function) minus integration of


(differentiation of first) into (integration of second).
Integration by parts:
Integration by parts:

Which is first function u or v ?


'ILATE' Rule: Increasing Ease of Integration
I - Inverse Trigonometric function
L - Logarithmic function
A - Algebraic function
T - Trigonometric function
E - Exponential function.
Type 1: Two separate functions are visible

Example: Evaluate : ∫x.tan-1 x dx


A.

B.

C.

D.
Type 2: Considering ‘1’ as a function

Example: Evaluate : ∫lnx dx


Type 3: Deja Vu

Example: Evaluate : ∫e2x sinx dx


Important Formulas:
Type 4: Direct Result-1

Note:
Type 4: Direct Result-1

Example: Evaluate:
Type 4: Direct Result-1

Example: Evaluate:
Type 5: Direct Result -2

Note:
Type 5: Direct Result -2

Example: Evaluate:
2014
A. B.

C. D.
D.I. Method
(Shortcut)
Recurring By Parts (D.I. Method)

This method (shortcut) is helpful if the integral is of the type


Evaluate:
Evaluate:
Integration by Parts:
Practice Problems
A. B.

C. D.
dx is equal to
is equal to

2013
A. B.

C. D.
The integral dx is equal to

(where C is a constant of integration)

A.

B.

C.

D.
is equal to

A. B.

C. D.
Formula Set-3:
Based on By Parts
Formula Set -3 : Based on By Parts

1.
Formula Set -3 : Based on By Parts

2.
Formula Set -3 : Based on By Parts

3.
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