Question

How to do questions of integration related to logarithms?

Answer 1

Answer:

Explanation:We use f(x)=\ln(x)f(x)=ln(x) and g'(x)=1g  

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(x)=1, which means that g(x)=xg(x)=x. Plugging these into our integration by parts formula, we get

\begin{aligned} \int 1 \cdot \ln(x)\ dx&=x \ln(x) - \int \big(\ln(x)\big)' x\ dx\\&=x \ln(x) - \int \frac{x}{x}\ dx\\&=x \ln(x) - x + C. \end{aligned}

∫1⋅ln(x) dx

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=xln(x)−∫(ln(x))  

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x dx

=xln(x)−∫  

x

x

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 dx

=xln(x)−x+C.

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