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Question
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
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Solution
To find the value of `int ((1 + log x))/x dx` the proper substitution is 1 + log x = t.
Explanation:
Given integral is `int ((1 + log x) )/x dx`
Let t = 1 + log x
Differentiate w.r.t. x we get,
`dt/dx = 1/x`
⇒ dx = x dt
Now substitute into the integral:
`int t/x dx`
= `int t/x * x dt`
= `∫ t dt`
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