Find $\displaystyle\int \frac{(25x^4 + 4)}{\sqrt{x}} \, \mathrm{d}x$.[2] Express \(\frac{4x - 3}{4

Question

Find $\displaystyle\int \frac{(25x^4 + 4)}{\sqrt{x}} \, \mathrm{d}x$.[2] Express $\frac{4x - 3}{4 - x}$ in the form $A + \frac{B}{4 - x}$, where $A$ and $B$ are integers. Hence find $\displaystyle\int \frac{4x - 3}{4 - x} \, \mathrm{d}x$, where $x < 4$.[3]

Accepted Answer

(a)$\frac{50}{9}x^{\frac{9}{2}}+8x^{\frac{1}{2}}+c$ (b)$- 4+\frac{13}{4-x}$,$-4x-13\ln | 4-x |+c$

2024 ACJC H1 Q3

2024 ACJC H1 Q3