Question
Evaluate:
$\int\text{x log 2x dx}$.
$\int\text{x log 2x dx}$.
= $\frac{\text{x}^{2}}{2}\cdot\log\text{2x}-\frac{1}{2}\int\text{x dx + c}_{1}=\frac{\text{x}^{2}}{2}\cdot\log\text{ 2x}-\frac{\text{x}^{2}}{4}+\text{c}.$
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| Values of X: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| P(X) | a | 3a | 5a | 7a | 9a | 11a | 13a | 15a | 17a |
Determine:
$\text{P}(\text{X}<3),\text{P}(\text{X}\geq3),\text{P}(0<\text{X}<5).$$\int\frac{\log(\text{x}+2)}{(\text{x}+2)^2}\text{dx}$
$\int2\text{x}^3\text{e}^{\text{x}^{2}}\text{dx}$