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Popular >

integral of 2x+5x^{-2}

Solution

\int 2 x + 5 x^{- 2} d x

Solution

x^{2} - \frac{5}{x} + C

Solution steps

\int 2 x + 5 x^{- 2} d x

5 x^{- 2} = \frac{5}{x ^{2}}

= \int 2 x + \frac{5}{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{5}{x ^{2}} d x

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

\int \frac{5}{x ^{2}} d x = - \frac{5}{x}

= x^{2} - \frac{5}{x}

Add a constant to the solution

= x^{2} - \frac{5}{x} + C

Popular Examples

(d^2)/(dx^2)(17e^{x^2})

\frac{d ^{2}}{d x ^{2}} (17 e^{x^{2}})

integral of (7x^3-7)^4x^2

\int (7 x^{3} - 7)^{4} x^{2} d x

derivative of sqrt(x^2-2x+3)

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

derivative of \sqrt[3]{(x^2-4^2})

limit as x approaches-1 of x/(5sin(x+1))

x \to - 1 lim (\frac{x}{5 sin ( x + 1 )})

Frequently Asked Questions (FAQ)

What is the integral of 2x+5x^{-2} ?
The integral of 2x+5x^{-2} is x^2-5/x+C