How do I evaluate $\int (13 x^{2} + 12 x^{- 2}) d x$ $int(13 x^2 + 12 x^-2)dx$ ?

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How do I evaluate $\int (13 x^{2} + 12 x^{- 2}) d x$ $int(13 x^2 + 12 x^-2)dx$ ?

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Answer 1 · 2015-01-27T20:32:33

I would use the integral of a sum

$\int f (x) + g (x) d x = \int f (x) d x + \int g (x) d x$ $intf(x)+g(x)dx=intf(x)dx+intg(x)dx$

to divide the argument of the igral giving:

$\int 13 x^{2} d x + \int 12 x^{- 2} d x =$ $int13x^2dx+int12x^-2dx=$

and integrating:

$\frac{13 x^{2 + 1}}{2 + 1} + \frac{12 x^{- 2 + 1}}{- 2 + 1} = \frac{13}{3} x^{3} - \frac{12}{x} + c$ $(13x^(2+1))/(2+1)+(12x^(-2+1))/(-2+1)=13/3x^3-12/x+c$

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How do I evaluate $\int (13 x^{2} + 12 x^{- 2}) d x$ $int(13 x^2 + 12 x^-2)dx$ ?

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