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Question

Find the integral 2xx24dx

A
ln(2x)+C
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B
ex24+C
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C
ln(x24)+C
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D
ex242x+C
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Solution

The correct option is C ln(x24)+C
Given, f(x)=2xx24
So, to integrate the given function we use substitution method.
Let t=x24 dtdx=2x
Or, dt=2xdx
Thus, substituting this value in the given function we have,
2xx24dx=1tdt=lnt+C
ln(x24)+C

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