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Numerade Educator

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Problem 27 Easy Difficulty

Find $ f $.

$ f"(x) = 2x + 3e^x $

Answer

$$
f(x)=\frac{x^{3}}{3}+3 e^{x}+c x+d
$$

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Video Transcript

So here, given um F double prime of X as to X plus three E D X. Yeah. Yeah. We want to find F prime of X and F ultimately so F prime of X is going to be the anti derivative of two acts, which is X squared plus the anti derivative of three E V X, which is just three E X. Then we want to find F of X which is equal to, we know that the anti derivative of X squared is going to be X cubed over three. And the anti derivative of free E to the X is once again going to be three E to the X. But we have to remember those constant values. So when we took the first anti derivative we would get plus C, which means here for our second anti derivative would get plus C. X. And then plus another constant D. So this right here would be our final answer.