Question:
Evaluate
\[
\int e^{x^2} (2x + x^3) (3 + x^2)^2 \, dx
\]
Evaluate
\[ \int e^{x^2} (2x + x^3) (3 + x^2)^2 \, dx \]
\[ \int e^{x^2} (2x + x^3) (3 + x^2)^2 \, dx \]
Show Hint
Look for quotient-rule reverse patterns in integrals.
Updated On: Mar 23, 2026
- \(\dfrac{e^{x^2}}{3+x^2}+k\)
- \(\dfrac{1}{2}\dfrac{e^{x^2}}{(3+x^2)^2}+k\)
- \(\dfrac{1}{4}\dfrac{e^{x^2}}{(3+x^2)^2}+k\)
- \( \frac{1}{2} \, d \left( e^{x^2} (3 + x^2 + k) \right) \)
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The Correct Option is D
Solution and Explanation
Step 1: \((d)/(dx)(3+x²)=2x\)
Step 2: Recognise derivative form: \((d)/(dx)(fraceˣ²3+x²) =fraceˣ²(2x+x³)(3+x²)²\)
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