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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
Methods of Integration 12-31
Example 12.41 Evaluate
dx
x2 3 1sin
.
Solution: Here a = -1, b = 2 and n = 3. Also a < b.
So we apply the formula
dx
a b nx
n b a
a
nx
b
b a
+
=
+
sin
tanh
tan
2
2
2 2
1
2 2

+
=
+
c
dx
x
x
2 3 1
2
3 2 1
3
2
2
2 1
2 2
1
2 2
sin
( ) ( )
tanh
tan
( )

+
=
+
c
x
c
2
3 3
3
2
2
3
1
tanh
tan
.
Example 12.42 Evaluate
dx
x5 3+
sin
.
Solution: Here a = 5, b = 3 and n = 1. Also a > b.
So, we have
dx
a b nx
n a b
a
nx
b
a b
+
=
+
+
sin
tan
tan
2
2
2 2
1
2 2
cc
dx
x
x
5 3
2
1 5 3
1
5 3
5
2
3
2 2
1
2 2
+
=
+
sin
( )
tan tan

+
=
+
+
c
x
c
1
2
5
2
3
4
1
tan
tan
.
Evaluation of
dx
a b nx c nx+ +
sin ...
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Publisher Resources

ISBN: 9789353948221