Answer:
Take 1+x
5/2
=t
2
⇒
5
x
3/2
dx=2t dt
Rewrite the given integral as
⇒∫x
(1+x
)
1/2
dx
Substitutng t we get
4
∫(t
−1)
.t
dt
−2t
+1).t
6
+t
)dt
(
7
t
−
2t
+
3
)+C
35
4t
25
8t
15
+C
5/2)
7/2
8
Comparing this with given expression we get
P=
,Q=
−8
,R=
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Answers & Comments
Answer:
Take 1+x
5/2
=t
2
⇒
2
5
x
3/2
dx=2t dt
Rewrite the given integral as
⇒∫x
5
(1+x
5/2
)
1/2
x
3/2
dx
Substitutng t we get
⇒
5
4
∫(t
2
−1)
2
.t
2
dt
⇒
5
4
∫(t
4
−2t
2
+1).t
2
dt
⇒
5
4
∫(t
6
−2t
4
+t
2
)dt
⇒
5
4
(
7
t
7
−
5
2t
5
+
3
t
3
)+C
⇒
35
4t
7
−
25
8t
5
+
15
4t
3
+C
⇒
35
4
(1+x
5/2)
7/2
−
25
8
(1+x
5/2
)
5/2
+
15
4
(1+x
5/2
)
3/2
+C
Comparing this with given expression we get
P=
35
4
,Q=
25
−8
,R=
15
4