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F(x)=x(2+x^2)^2 Answer: ((x^2+2)^3)/(6)+C

Question

f(x)=x(2+x^2)^2 Answer: ((x^2+2)^3)/(6)+C

Solution

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Zoe Veteran ยท Tutor for 12 years

Answer

The provided answer is incorrect. Let's find the correct integral of .We can solve this using substitution. Let . Then, the derivative of with respect to is , which means , or .Now, substitute and into the integral: Now, integrate with respect to : Finally, substitute back the original expression for : Therefore, the correct answer is .