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Popular Calculus >

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

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

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

(sqrt(x)cos(sqrt(x)))^'

(x cos (x))^{^{'}}

integral of cos(x)sec^2(x)

\int cos (x) sec^{2} (x) d x

f (x) = - sec^{2} (x)

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