Integration using partial fractions

Integration using partial fractions Quiz

Spec 6.3 · Edexcel International A Level Maths: Quiz

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  1. 1. Find ∫52x+1 dx\int\frac{5}{2x+1}\,dx.

    • A. 52ln⁡∣2x+1∣+c\frac52\ln|2x+1|+c
    • B. 5ln⁡∣2x+1∣+c5\ln|2x+1|+c
    • C. 25ln⁡∣2x+1∣+c\frac25\ln|2x+1|+c
    • D. −52(2x+1)2+c-\frac{5}{2(2x+1)^2}+c

  2. 2. Find ∫4(x+2)2 dx\int\frac{4}{(x+2)^2}\,dx.

    • A. 4ln⁡∣x+2∣+c4\ln|x+2|+c
    • B. 4x+2+c\frac{4}{x+2}+c
    • C. −4(x+2)3+c-\frac{4}{(x+2)^3}+c
    • D. −4x+2+c-\frac{4}{x+2}+c

  3. 3. Using 3(x−1)(x+2)=1x−1−1x+2\frac{3}{(x-1)(x+2)}=\frac{1}{x-1}-\frac{1}{x+2}, find ∫233(x−1)(x+2) dx\int_2^3\frac{3}{(x-1)(x+2)}\,dx.

    • A. ln⁡58\ln\frac58
    • B. ln⁡85\ln\frac85
    • C. ln⁡25\ln\frac25
    • D. ln⁡45\ln\frac45

  4. 4. What is the correct form of partial fractions for x+7(x+1)(x−3)2\frac{x+7}{(x+1)(x-3)^2}?

    • A. Ax+1+Bx−3\frac{A}{x+1}+\frac{B}{x-3}
    • B. Ax+1+B(x−3)2\frac{A}{x+1}+\frac{B}{(x-3)^2}
    • C. Ax+1+Bx−3+C(x−3)2\frac{A}{x+1}+\frac{B}{x-3}+\frac{C}{(x-3)^2}
    • D. Ax+1+Bx+Cx−3\frac{A}{x+1}+\frac{Bx+C}{x-3}

  5. 5. Simplify 2ln⁡3+ln⁡22\ln3+\ln2.

    • A. ln⁡12\ln12
    • B. ln⁡36\ln36
    • C. ln⁡7\ln7
    • D. ln⁡18\ln18

Quiz