Problem

Find antiderivatives of the given functions. $$f(…

Problem 27 Easy Difficulty

Find antiderivatives of the given functions.
$$f(x)=x^{2}-4+x^{-2}$$

Answer

$\frac{x^{3}}{3}-4 x-\frac{1}{x}$

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 25

Integration

Section 1

Antiderivatives

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Video Transcript

mm We want to find the anti derivative of the function F of X is equal to X square minus four plus. Excellent. Second. This question is testing our knowledge of anti differentiation as appreciated. Integration. Uh said, we must have a solid understanding of this concept to proceed. So remember that the anti derivative is just the inverse derivative function. So if we know the rules for decorative taken, we know how to take the time derivative by the inverse for this problem. Out of the rules 123 listed on the right. We only need to use rule one. The power rule, which states would rhythms that G D xx today is A X to the a minus one. Therefore by the inverse, the end of the river of ex D. A is 1/8 plus one. Actually the A plus one. Therefore we can solve for capital Fx and derivatives as follows. Capital fx is one third X cubed minus four X plus negative one. Excellent negative one. We use the power rule or the inverse power rule on all three in the middle terms and there was no value except to add value X, which is 1/0 plus one, actually zero plus one. This gives us final solution. F x equals X cubed over three minus four X minus X negative first.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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