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Integrate dx / ((x-2)² * (x²+4))

March 21, 2026Mathematics

ScanSolve AI Answer

Answer

\dfrac{x-2}{x^{2}+5}

3 steps

Rewrite the complex fraction as a single fraction.
$\frac{ \frac{x^{2} - 2x}{x} }{ x^{2} + 5 } = \frac{x^{2} - 2x}{x(x^{2} + 5)}$
Factor the numerator.
$x^{2} - 2x = x(x - 2)$
Substitute into the fraction:
$\frac{x(x - 2)}{x(x^{2} + 5)}$
Cancel the common factor $x$ (for $x \neq 0$ ).
$\frac{x - 2}{x^{2} + 5}$
\dfrac{x-2}{x^{2}+5}

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