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Popular >

integral of 2x+7x^{-2}

Solution

\int 2 x + 7 x^{- 2} d x

Solution

x^{2} - \frac{7}{x} + C

Solution steps

\int 2 x + 7 x^{- 2} d x

7 x^{- 2} = \frac{7}{x ^{2}}

= \int 2 x + \frac{7}{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{7}{x ^{2}} d x

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

\int \frac{7}{x ^{2}} d x = - \frac{7}{x}

= x^{2} - \frac{7}{x}

Add a constant to the solution

= x^{2} - \frac{7}{x} + C

Graph

Popular Examples

(d^2)/(dx^2)(8x+15)

\frac{d ^{2}}{d x ^{2}} (8 x + 15)

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\int_{0}^{3} (x - 1)^{2} d x

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\int \frac{x + 6}{( x ^{2} + 6 ) ( x ^{2} + 1 )} d x

limit as x approaches 0 of x+|x|

x \to 0 lim (x + ∣ x ∣)

Frequently Asked Questions (FAQ)

What is the integral of 2x+7x^{-2} ?
The integral of 2x+7x^{-2} is x^2-7/x+C