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NDA Math Indefinite Integrals
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© examsnet.com
Question : 34
Total: 38
What is
∫
x
e
x
d
x
(
x
+
1
)
2
equal to ?
where c is the constant of integration
[NDA I 2015]
(
x
+
1
)
2
e
x
+
c
(
x
+
1
)
e
x
+
c
e
x
x
+
1
+
c
e
x
(
x
+
1
)
2
+
c
Validate
Solution:
∫
x
e
x
(
x
+
1
)
2
d
x
=
∫
(
x
+
1
)
e
x
−
e
x
(
x
+
1
)
2
d
x
∫
e
x
(
x
+
1
)
d
x
−
∫
e
x
(
x
+
1
)
2
d
x
=
I
1
−
I
2
I
1
=
∫
e
x
(
x
+
1
)
d
x
=
e
x
(
x
+
1
)
+
∫
e
x
(
x
+
1
)
2
d
x
+
c
(Using integration by parts)
∴
I
=
I
1
+
I
2
=
e
x
(
x
+
1
)
+
∫
e
x
(
x
+
1
)
2
d
x
−
∫
e
(
x
+
1
)
2
d
x
+
c
e
x
(
x
+
1
)
+
c
⇒
I
=
e
x
(
x
+
1
)
+
c
© examsnet.com
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