Question

Evaluate int fraceˣ²(2x+x³)(3+x²)²dx

• A. \(\dfrac{e^{x^2}}{3+x^2}+k\)
• B. \(\dfrac{1}{2}\dfrac{e^{x^2}}{(3+x^2)^2}+k\)
• C. \(\dfrac{1}{4}\dfrac{e^{x^2}}{(3+x^2)^2}+k\)
• D. (1)/(2)dfraceˣ²3+x²+k

Hint:

Look for quotient-rule reverse patterns in integrals.

Answer 1

The Correct Option is D

Step 1: (d)/(dx)(3+x²)=2x
Step 2: Recognise derivative form: (d)/(dx)(fraceˣ²3+x²) =fraceˣ²(2x+x³)(3+x²)²