Question:
Evaluate: $\int \frac{1}{2-3 x}+\frac{1}{\sqrt{3 x-2}} d x$
Solution:
Let I $=\int \frac{1}{2-3 x}+\frac{1}{\sqrt{3 x-2}} d x$
$\mathrm{I}=\int \frac{1}{2-3 \mathrm{x}}+\frac{1}{\sqrt{3 \mathrm{x}-2}} \mathrm{dx}$
We know $\int \frac{1}{x} d x=\log |x|+C$
$=\frac{\log |2-3 x|}{-3}+\frac{2}{3}(3 x-2)^{\frac{1}{2}}$
$=-\frac{1}{3} \mathrm{x} \cdot \log |2 \mathrm{x}-3|+\frac{2}{3} \sqrt{3 \mathrm{x}-3}+\mathrm{C}$
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