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Numerade Educator

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Problem 22 Easy Difficulty

Find the most general antiderivative of the function.
(Check your answers by differentiation.)

$ f(x) = \dfrac{2x^2 + 5}{x^2 + 1} $

Answer

$$
2 x+3 \arctan x+C
$$

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Video Transcript

So keeping in mind that this right here the anti derivative is the arc tangent of axe. When we have F of X equals two X squared. That's five over X squared plus one. I take the anti derivative of this F of X. What we see is that um the general anti derivative since this right here is equal to um we could write this as two X squared plus one. This can be written as to plus three over X squared plus one. That's because if we got a common denominator, there'll be two X squared plus two and then plus three is the five. So now we can write this as two acts plus three times we are tangent of X. And then we have to remember to add that constant C. At the end of it. So that should be our final anti derivative.