integration using partial fractions

**twilightstr** · February 4th 2009, 12:41 AM

integrate 1/(x^(1/2) - x^(1/3)). I only that i should substitute u for x^(1/6)

**mr fantastic** · February 4th 2009, 03:26 AM

Originally Posted by twilightstr

integrate 1/(x^(1/2) - x^(1/3)). I only that i should substitute u for x^(1/6)

$\int \frac{1}{x^{1/2} - x^{1/3}} \, dx = \int \frac{1}{u^3 - u^2} \, (6 u^5 \, du) = 6 \int \frac{u^3}{u - 1} \, du = 6 \int u^2 + u + 1 + \frac{1}{u-1} \, du$

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