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Popular >

integral of 2x+4x^{-2}

Solution

\int 2 x + 4 x^{- 2} d x

Solution

x^{2} - \frac{4}{x} + C

Solution steps

\int 2 x + 4 x^{- 2} d x

4 x^{- 2} = \frac{4}{x ^{2}}

= \int 2 x + \frac{4}{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{4}{x ^{2}} d x

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

\int \frac{4}{x ^{2}} d x = - \frac{4}{x}

= x^{2} - \frac{4}{x}

Add a constant to the solution

= x^{2} - \frac{4}{x} + C

Popular Examples

limit as x approaches 6 of 9x+|x-6|

x \to 6 lim (9 x + ∣ x - 6 ∣)

integral of x/(sqrt(8-x^2))

\int \frac{x}{8 - x ^{2}} d x

derivative of y=3^x derivative of

y = 3^{x}

(dy)/(dx)=(xy+y+x+1)/(xy+2x-y-2)

\frac{d y}{d x} = \frac{x y + y + x + 1}{x y + 2 x - y - 2}

derivative of (x-4/(-x^2+4))

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

Frequently Asked Questions (FAQ)

What is the integral of 2x+4x^{-2} ?
The integral of 2x+4x^{-2} is x^2-4/x+C