Indefinite Integration
Integration with Exponentials
Grade 12
Question:
<p>The value of $\displaystyle \int \frac{dx}{x(1+xe^x)^2}$ is equal to</p>
<p>(A) $\ln \left|\frac{xe^x}{1+xe^x}\right| + C$</p>
<p>(B) $\ln \left|\frac{xe^x}{1+xe^x}\right| + C$</p>
<p>(C) $\ln \left|\frac{xe^x}{1+e^x}\right| + C$</p>
<p>(D) none of these</p>
Step-by-Step Solution
Key Concept: Identify the relationship between numerator and denominator to apply logarithmic integration
<p>This integral requires recognizing the structure and using appropriate substitution or partial fractions.</p>
Correct Answer: A