(i) Express $\dfrac{8x}{2x+3}$ in the form $a+\dfrac{b}{2x+3}$, where $a$ and $b$ are intege

Question

(i) Express $\dfrac{8x}{2x+3}$ in the form $a+\dfrac{b}{2x+3}$, where $a$ and $b$ are integers. (ii) Differentiate $4x\ln(2x+3)$ with respect to $x$. (iii) Hence evaluate the exact value of $\displaystyle\int_0^1\ln(2x+3)\,\mathrm{d}x$.

Accepted Answer

$\dfrac52\ln5-\dfrac32\ln3-1$

Solution:

Solution locked