I just want to see if I got this correct. From what all I've read it seems that I have most of it understood, but eh, I don't trust my judgement...(adsbygoogle = window.adsbygoogle || []).push({});

Lets say we have [tex]f(x) = {{3x^3 + 8x^2 + 7x + 12} \over {4x^2 - 12x - 15}}[/tex]

And the derivative...

[tex]

{d \over dx} f(x) = \lim _{h \rightarrow 0} {{f(x+h) - f(x)} \over h} =

{{

{d \over dx} (3x^3 + 8x^2 + 7x + 12)

}

\over

{

{d \over dx} (4x^2 - 12x - 15)

}} = f'(x)

[/tex]

Thus the integral would be...

[tex]

\int {f'(x)} \textbf{ }dx = f(x)

[/tex]

And if the constants are unknown, thus letting a and b represent the constants...

[tex]

\int {f'(x)} \text{ } dx = {{3x^3 + 8x^2 + 7x + a} \over {4x^2 - 12x + b}}

[/tex]

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# Derivatives and Integrals

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