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

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

ScanSolve AI Answer

Answer

x−2x2+5\dfrac{x-2}{x^{2}+5}

Step 1: Rewrite the complex fraction as a single fraction.

x2−2xxx2+5=x2−2xx(x2+5)\frac{ \frac{x^{2} - 2x}{x} }{ x^{2} + 5 } = \frac{x^{2} - 2x}{x(x^{2} + 5)}

Step 2: Factor the numerator.

x2−2x=x(x−2)x^{2} - 2x = x(x - 2)

Substitute into the fraction:

x(x−2)x(x2+5)\frac{x(x - 2)}{x(x^{2} + 5)}

Step 3: Cancel the common factor xx (for x≠0x \neq 0).

x−2x2+5\frac{x - 2}{x^{2} + 5}

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

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.

More Mathematics Questions

QPlease Draw Using a ruler and a pair of compases Only construct the following angles 5° 135°QJournal riyazi TCS School maliya malayatti riyasi chapter ka naam hai aur is chapter mein 4.1 exerci…QQUESTION 2 John decided to start a car wash service on Saturdays in his matric year. He rented a Pow…QDetermine the values of A & BQExplain the following (i) what a statistical hypothesis is, (ii) an estimator and an estimate (iii)…
See all Mathematics questions →

Still have questions?

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.

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

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 Answer
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