Question
Evaluate the following integrals:
$\int\frac{\text{e}^{2\text{x}}}{1+\text{e}^\text{x}}\text{ dx}$
$\int\frac{\text{e}^{2\text{x}}}{1+\text{e}^\text{x}}\text{ dx}$
$=\int\frac{(\text{t}-1)\text{dt}}{\text{t}}$
$=\Big(1-\frac{1}{\text{t}}\Big)\text{dt}$
$=\text{t}-\log|\text{t}|+\text{C}$
$=\big(1+\text{e}^\text{x}\big)-\log\big(1+\text{e}^\text{x}\big)+\text{C}$
Let $\text{C}+1=\text{C}^\text{n}$ $=\text{e}^\text{x}-\log\big(1+\text{e}^\text{x}\big)+\text{C}^\text{n}$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $\text{x}_\text{i}$ | $-5$ | $-4$ | $1$ | $2$ |
| $\text{p}_\text{i}$ | $\frac{1}{4}$ | $\frac{1}{8}$ | $\frac{1}{2}$ | $\frac{1}{8}$ |