PYQ Vault

x or x^3 over (x^2 + a)(x^2 + b): substitute t = x^2, then partial fractions

This type of question, asked 2 times: 22 Apr 2025 S2, 20 Apr 2026 S1. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    22 Apr 2025 S2

    114
    ∫x3x4+5x2+4 dx=\int\frac{x^{3}}{x^{4}+ 5x^{2}+ 4}\text{ }dx =

    Tap an option to check your answer.

  2. Question 2

    20 Apr 2026 S1

    77
    If f(x)=∫x(x2+4)(x2+9) dxf(x) = \displaystyle\int\dfrac{x}{(x^2 + 4)(x^2 + 9)}\,dx and f(0)=15log⁡(23)f(0) = \dfrac{1}{5}\log\left(\dfrac{2}{3}\right), then f(1)=f(1) =

    Tap an option to check your answer.