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Popular >

integral of 2x+6x^{-2}

Solution

\int 2 x + 6 x^{- 2} d x

Solution

x^{2} - \frac{6}{x} + C

Solution steps

\int 2 x + 6 x^{- 2} d x

6 x^{- 2} = \frac{6}{x ^{2}}

= \int 2 x + \frac{6}{x ^{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x d x + \int \frac{6}{x ^{2}} d x

\int 2 x d x = x^{2}

\int \frac{6}{x ^{2}} d x = - \frac{6}{x}

= x^{2} - \frac{6}{x}

Add a constant to the solution

= x^{2} - \frac{6}{x} + C

Graph

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\frac{d}{d x} (\frac{x ^{4} - 3 x ^{2}}{( x ^{2} - 1 ) ^{2}})

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x = \frac{( y - 2 ) ^{2}}{2}, y = 6 - x

Frequently Asked Questions (FAQ)

What is the integral of 2x+6x^{-2} ?
The integral of 2x+6x^{-2} is x^2-6/x+C