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Popular >

integral of 2x+8x^{-2}

Solution

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

Solution

x^{2} - \frac{8}{x} + C

Solution steps

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

8 x^{- 2} = \frac{8}{x ^{2}}

= \int 2 x + \frac{8}{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{8}{x ^{2}} d x

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

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

= x^{2} - \frac{8}{x}

Add a constant to the solution

= x^{2} - \frac{8}{x} + C

Popular Examples

tangent of f(x)=x^2+10x,\at x=8 tangent of

f (x) = x^{2} + 10 x, at x = 8

limit as x approaches infinity of x^2e^{2x}

x \to \infty lim (x^{2} e^{2 x})

limit as x approaches-2 of (x^3+1)/(x+1)

x \to - 2 lim (\frac{x ^{3} + 1}{x + 1})

y^{''}-3y^'+2y=14sin(2x)+18cos(2x)

y^{^{''}} - 3 y^{^{'}} + 2 y = 14 sin (2 x) + 18 cos (2 x)

derivative of 3x^5-2x^4-4x^3

\frac{d}{d x} (3 x^{5} - 2 x^{4} - 4 x^{3})

Frequently Asked Questions (FAQ)

What is the integral of 2x+8x^{-2} ?
The integral of 2x+8x^{-2} is x^2-8/x+C