Integration using partial fractions and reverse chain rule

Integration using partial fractions and reverse chain rule Quiz

Spec 8.5–6 · Edexcel A-Level Maths: Quiz

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  1. 1. Find ∫6x22x3+1 dx\int\frac{6x^2}{2x^3+1}\,\mathrm{d}x.

    • A. 6x2ln⁡∣2x3+1∣+c6x^2\ln|2x^3+1|+c
    • B. 12ln⁡∣2x3+1∣+c\frac12\ln|2x^3+1|+c
    • C. ln⁡∣2x3+1∣+c\ln|2x^3+1|+c
    • D. −1(2x3+1)2+c-\frac{1}{(2x^3+1)^2}+c

  2. 2. Find ∫2(2x−1)4 dx\int\frac{2}{(2x-1)^4}\,\mathrm{d}x.

    • A. −13(2x−1)3+c-\frac{1}{3(2x-1)^3}+c
    • B. −23(2x−1)3+c-\frac{2}{3(2x-1)^3}+c
    • C. 12x−1+c\frac{1}{2x-1}+c
    • D. −1(2x−1)3+c-\frac{1}{(2x-1)^3}+c

  3. 3. Write x+7(x+1)(x−2)\frac{x+7}{(x+1)(x-2)} in partial fractions.

    • A. 3x+1−2x−2\frac{3}{x+1}-\frac{2}{x-2}
    • B. 2x+1+3x−2\frac{2}{x+1}+\frac{3}{x-2}
    • C. −3x+1+2x−2\frac{-3}{x+1}+\frac{2}{x-2}
    • D. −2x+1+3x−2-\frac{2}{x+1}+\frac{3}{x-2}

  4. 4. Find the exact value of ∫012xx2+1 dx\int_0^1\frac{2x}{x^2+1}\,\mathrm{d}x.

    • A. ln⁡1\ln1
    • B. ln⁡2\ln2
    • C. 2ln⁡22\ln2
    • D. 12ln⁡2\frac12\ln2

  5. 5. Find ∫32x+1 dx\int\frac{3}{2x+1}\,\mathrm{d}x for x>−12x>-\frac12.

    • A. 3ln⁡(2x+1)+c3\ln(2x+1)+c
    • B. 6ln⁡(2x+1)+c6\ln(2x+1)+c
    • C. 32ln⁡(2x+1)+c\frac32\ln(2x+1)+c
    • D. −3(2x+1)2+c-\frac{3}{(2x+1)^2}+c

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