CUET · MATHS · PYQ PAPER 2023
The integral \(\int \frac{2 x+x^3}{1+x^2} d x\) is equal to :
- A \(\log \left(1+x^2\right)+x+C\) where \(C\) is a constant of integration
- B \(\frac{1}{2} \log \left(1+x^2\right)+x^2+C\) where \(C\) is a constant of integration
- C \(\frac{1}{2} \log \left(1+x^2\right)+\frac{1}{2} x+C\) where \(C\) is a constant of integration
- D \(\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C\) where \(C\) is a constant of integration
Answer & Solution
Correct Answer
(D) \(\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C\) where \(C\) is a constant of integration
Step-by-step Solution
Detailed explanation
\(\int \frac{2 x+x^3}{1+x^2} d x = \int \left( x + \frac{x}{x^2+1} \right) d x\) \(\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C\)
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