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If $\int f (x) dx = f (x) + C, then \int {f (x)}^{2} dx$ is

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{f(x)}2+C

13{f(x)}3+C

f(x)+C

12{f(x)}2+C

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detailed solution

Correct option is D

Given,∫f(x)dx=f(x)+Cf(x)=f′(x)∴∫f(x)2dx=∫f(x)⋅f′(x)dx=12{f(x)}2+C

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If ∫f(x)dx=f(x)+C, then ∫{f(x)}2dx is

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If $\int f (x) dx = f (x) + C, then \int {f (x)}^{2} dx$ is