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Calculus: Differentiation and Integration, 1st Edition
book

Calculus: Differentiation and Integration, 1st Edition

by ICFAI
April 2024
Intermediate to advanced content levelIntermediate to advanced
710 pages
20h 50m
English
Pearson India
Content preview from Calculus: Differentiation and Integration, 1st Edition
13-16  Calculus – Differentiation and Integration
Comparing the coefficients of powers of x on both sides, we get
1
3 2 4
4 4
1 1
1 2 1
1
= +
= + +
=
A B
A A B
B ( ).Step 5
After solving the above system of linear equations with four unknowns, we get
A A B
1 2 1
2 3 1= = = , , ( ).Step 6
Substituting the above values in Eq. (1) and integrating on both sides, we get
x x
x x
dx
x
dx
x
dx
x
dx
x
2
2 2
3 4
2
2
2
3
2
1
2 2
+
=
+
+
= +
( ) ( )
( )
ln(
Step 7
)) ln .+
+
+
3
2x
x c
Example 13.19 Evaluate
x
x x
dx
+
1
1 2
3
( ) ( )
.
Solution: Observe that the linear factor (x - 1) is repeated thrice in the denominator
1
1
1
1 1
3
1 2
2
3
3
( ) ( ) ( )
( ).
x
A
x
A
x
A
x
=
+
+
Step 1
Assign the non-repeated ...
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Publisher Resources

ISBN: 9789353948221