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GUJCET 2019 Math Solved Paper
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© examsnet.com
Question : 14
Total: 40
∫ ( 2 + logx)
(
e
x
)
x
dx ..….. + C ; x > 1
(
e
x
)
x
x
x
(
e
x
)
–
x
e
x
x
Validate
Solution:
(A)
Let
(
e
x
)
x
= t
x
l
n
ex =
l
n
t
x(1 +
l
n
x) =
l
n
t
(
x
⋅
1
x
+
(
1
+
l
n
x
)
)
dx =
1
t
dt
(
e
x
)
x
(2 + lnx)dx =
1
t
dt
∫dt = t + c ⇒
(
e
x
)
x
+ c
© examsnet.com
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