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BenoguigoliB

Answered question

2021-05-02

Evaluate the integral. (Use C for the constant of integration.)

\int \ln (\sqrt{x}) d x

Macsen Nixon

Skilled2021-05-03Added 117 answers

I solved the integral:

Jeffrey Jordon

Expert2021-09-09Added 2605 answers

Solution:

$\int \ln (\sqrt{x}) d x = \int 1 \cdot \ln (\sqrt{x}) d x$

Now we apply integration by parts

$= [x \cdot \ln (\sqrt{x})] - \int \frac{1}{\sqrt{x}} (\frac{1}{2 \sqrt{x}}) \cdot x d x + C$

$= [x \ln (\sqrt{x})] - \int \frac{1}{2 x} \cdot x d x + C$

$= x \ln \sqrt{x} - \frac{1}{2} \int d x + C$

$\int \ln (\sqrt{x}) d x = x \ln \sqrt{x} - \frac{x}{2} + C$

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