Indefinite Integration
Rational Functions
JEE Main PYQ
Grade 12
Question:
If $\int \frac{3x^2 + 2x + 5}{x^2 + 1} \, dx = 3x + \lambda \tan^{-1} x + \ln(x^2 + 1) + C$, the value of $\lambda$ equals _____.
Step-by-Step Solution
Key Concept: Perform polynomial division on $\frac{3x^2 + 2x + 5}{x^2 + 1}$ first, then split the resulting proper fraction into a $\frac{x}{x^2 + 1}$ part and a $\frac{1}{x^2 + 1}$ part.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 2