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Popular >

integral of 1+1/(x^2)

Solution

\int 1 + \frac{1}{x ^{2}} d x

Solution

x - \frac{1}{x} + C

Solution steps

\int 1 + \frac{1}{x ^{2}} d x

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{x ^{2}} = x^{- 2}

= \int 1 + 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 1 d x + \int x^{- 2} d x

\int 1 d x = x

\int x^{- 2} d x = - \frac{1}{x}

= x - \frac{1}{x}

Add a constant to the solution

= x - \frac{1}{x} + C

Graph

Popular Examples

integral of-4x^2-12x+16

\int - 4 x^{2} - 12 x + 16 d x

derivative of (0.14x/(0.015+x))

\frac{d}{d x} (\frac{0.14 x}{0.015 + x})

integral of y-e^{cos(x)}sin(x)

\int y - e^{c o s (x)} sin (x) d x

integral of ((3x-5))/(x^3-5x^2-14x)

\int \frac{( 3 x - 5 )}{x ^{3} - 5 x ^{2} - 14 x} d x

derivative of \sqrt[3]{x^3+y^3}

\frac{d}{d x} (3 x^{3} + y^{3})

Frequently Asked Questions (FAQ)

What is the integral of 1+1/(x^2) ?
The integral of 1+1/(x^2) is x-1/x+C