Integrate dx / ((x-2)2 * (x2+4))

March 21, 2026Mathematics

ScanSolve AI Answer

March 21, 2026

Answer

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

Step 1: 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)}

Step 2: Factor the numerator.

x^{2} - 2x = x(x - 2)

Substitute into the fraction:

\frac{x(x - 2)}{x(x^{2} + 5)}

Step 3: 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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Quick Answer

Rewrite the complex fraction as a single fraction. x^2 - 2xx x^2 + 5 = x^2 - 2xx(x^2 + 5) Step 2: Factor the numerator.

Asked on March 21, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 21, 2026

Step 1: Rewrite the complex fraction as a single fraction. x^2 - 2xx x^2 + 5 = x^2 - 2xx(x^2 + 5) Step 2: Factor the numerator. x^2 - 2x = x(x - 2) Substitute into the fraction: (x(x - 2))/(x(x^2) + 5) Step 3: Cancel the common factor x (for x ≠ 0). (x - 2)/(x^2) + 5 (x-2)/(x^2)+5