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3 years ago

5

Integrate 1/x(x-1) dx

1 answer:

amm18123 years ago

7 0

Decompose the integrand into partial fractions:

1 / (<em>x</em> (<em>x</em> - 1)) = 1/(<em>x</em> - 1) - 1/<em>x</em>

Then

∫ 1 / (<em>x</em> (<em>x</em> - 1)) d<em>x</em> = ln|<em>x</em> - 1| - ln|<em>x</em>| + C = ln|1 - 1/<em>x</em>| + C

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