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Problem 20 Easy Difficulty

Find the general indefinite integral. Illustrate by graphing several members of the family on the same screen.

$ \displaystyle \int (e^x - 2x^2) \,dx $

Answer

$\int e^{x}-2 x^{2} d x=e^{x}-\frac{2 x^{3}}{3}+C$

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Video Transcript

we are asked to find the integral anti directive of E. To the x minus two X. Squared. Mhm TX. And instead of memorizing rules which you could do, I just like to think of what's derivative could give me E. To the X. And that's pretty easy because it's the only function, one of the only function whose derivative is itself uh drip of E. To the X. Is E. To the X. And then the other piece. That's your power rule where you add one to your experiment and divide by your new experiment or multiply by the reciprocal of your new Excellent. Then you just need to remember your plus seed and you have the correct answer now before just moving on, I want to point out that you can check, your answer is correct by taking the derivative of each piece and double checking that that's correct. It's a dream to be. To the exceeded the ex yeah 0 to 2 thirds. Execute two X squared. Yeah. And it's a drift of of a constant which is all this is equal to zero because we don't write plus zero up here because it won't change anything. That's why we need this plus C. So we are good circled in green is correct and we can move on.