Question:
The integral \( \int \frac{1 + x^2 + x^4}{(1 - x^3)(1 + x^3)} \, dx \) is equal to:
The integral \( \int \frac{1 + x^2 + x^4}{(1 - x^3)(1 + x^3)} \, dx \) is equal to:
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Use partial fraction decomposition when dealing with rational expressions for easier integration.
Updated On: Apr 7, 2026
- \( \tan^{-1}(x) + C \)
- \( \tan^{-1}(1 + x^2) + C \)
- \( \frac{1}{2} \log(1+x) - \log(1-x) + C \)
- \( \log(1 + x^3) + C \)
- \( \log(1 + x^2) + C \)
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The Correct Option is C
Solution and Explanation
Step 1: Simplify the integral: \[ \int \frac{1 + x^2 + x^4}{(1 - x^3)(1 + x^3)} \, dx. \] This can be solved by partial fraction decomposition.
Step 2: After simplification, the result is: \[ \frac{1}{2} \log(1+x) - \log(1-x) + C. \]
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