Question
Find the following integrals in Exercises:
$\int(4\text{ e}^{3\text{x}} + 1)\text{ dx}$
$\int(4\text{ e}^{3\text{x}} + 1)\text{ dx}$
✓
Answer
$\int\bigg(4\text{e}^{3\text{x}}+1\bigg)\text{dx}$
$=\int4\text{e}^{3\text{x}}\text{ dx}+\int1 \text{ dx}=4\int{e}^{3\text {x}}\text{ dx}+\text{x}$
$=4 \frac{\text{e}^{3\text{x}}}{3}+\text{x}+\text{c} \ \ \ \ \ \ \ \ \ \ \bigg[\because \text{e}^ \text{ax}\text{ dx}=\frac{\text{e}^\text{ax}}{\text{x}}\text{and}\int1\text{ dx}=\text{x}\bigg]$
$=\int4\text{e}^{3\text{x}}\text{ dx}+\int1 \text{ dx}=4\int{e}^{3\text {x}}\text{ dx}+\text{x}$
$=4 \frac{\text{e}^{3\text{x}}}{3}+\text{x}+\text{c} \ \ \ \ \ \ \ \ \ \ \bigg[\because \text{e}^ \text{ax}\text{ dx}=\frac{\text{e}^\text{ax}}{\text{x}}\text{and}\int1\text{ dx}=\text{x}\bigg]$
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