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Byju's Answer
Standard XII
Mathematics
Integration by Parts
∫exxxlog x 2+...
Question
∫
e
x
x
x
log
x
2
+
2
log
x
d
x
Open in App
Solution
Let
I
=
∫
e
x
x
x
log
x
2
+
2
log
x
d
x
=
∫
e
x
log
x
2
+
2
log
x
x
d
x
Here
,
f
(
x
)
=
log
x
2
⇒
f
'
(
x
)
=
2
log
x
x
put
e
x
f
(
x
)
=
t
⇒
e
x
log
x
2
=
t
Diff
both
sides
w
.
r
.
t
x
e
x
log
x
2
+
e
x
2
log
x
x
d
x
=
d
t
∴
I
=
∫
d
t
=
t
+
C
=
e
x
log
x
2
+
C
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Q.
∫
e
x
x
(
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⋅
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log
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)
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)
d
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Q.
If
∫
π
2
0
log
cos
x
d
x
=
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2
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, then
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