The integral ∫?? e? ⋅ x²(2 + log?x)dx equals
The integral ∫?? e? ⋅ x²(2 + log?x)dx equals
Option 1 -
e(4e + 1)
Option 2 -
4e² – 1
Option 3 -
e(4e – 1)
Option 4 -
e(2e – 1)
Asked by Shiksha User
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1 Answer
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Correct Option - 3
Detailed Solution:Let y = (ex)?
ln y = x ln (ex) = x [1 + ln x]
(1/y) (dy/dx) = (1) (1 + ln x) + x (1/x) = 2 + ln x
⇒ dy = (ex)? (2 + ln x)dx
∫? ² (ex)? (2 + log? x)dx = [ (ex)? ]? ² = (2e)² - (1e)¹ = 4e² - e
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