Indefinite Integration
General
Grade 12
Question:
Evaluate $\int \left( \frac{1}{8x+9} + e^{8x+9} \right) dx$
Step-by-Step Solution
Key Concept: General
<div>$\int \frac{1}{x} dx = \ln|x| + C \Rightarrow \int \frac{dx}{8x+9} = \frac{1}{8} \ln|8x+9| + C$<br>$\int e^x dx = e^x + C \Rightarrow \int e^{8x+9} dx = \frac{e^{8x+9}}{8} + C$<br>$\therefore \int \left( \frac{1}{8x+9} + e^{8x+9} \right) dx = \frac{\ln|8x+9| + e^{8x+9}}{8} + C$</div>
Correct Answer: A