Question:
\(\displaystyle \int \frac{3x^{2}+2}{x^{3}+2x}\,dx=\ \ ?\)
\(\displaystyle \int \frac{3x^{2}+2}{x^{3}+2x}\,dx=\ \ ?\)
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Try to see the denominator's derivative sitting upstairs.
Updated On: Oct 17, 2025
- \(\sin^{-1}(x^{3}+3x)+k\)
- \(\tan^{-1}(3x^{2}+2)+k\)
- \(\log|3x^{2}+2|+k\)
- \(\log|x^{3}+2x|+k\)
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The Correct Option is D
Solution and Explanation
Let \(g(x)=x^{3}+2x\Rightarrow g'(x)=3x^{2}+2\) (the numerator).
Therefore \(\int\dfrac{g'(x)}{g(x)}dx=\ln|g(x)|+k=\ln|x^{3}+2x|+k\).
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