Question
Download Solution PDFIntegrate: \(\rm \int \log x \ dx\).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Integration by Parts:
∫ f(x) g(x) dx = f(x) ∫ g(x) dx - ∫ [f'(x) ∫ g(x) dx] dx.
Definite Integral:
If ∫ f(x) dx = g(x) + C, then \(\rm \int_a^b f(x)\ dx = [ g(x)]_a^b\) = g(b) - g(a).
Calculation:
Let I = ∫ (1)(log x) dx.
Considering log x as the first function and 1 as the second function, we get:
= (log x) ∫ 1 dx - ∫ [\(\rm\frac1x\) ∫ 1 dx] dx
= (log x) x - x + C
= x (log x - 1) + C
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