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Popular >

integral of 2x+1/(x^2)

Solution

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

Solution

x^{2} - \frac{1}{x} + C

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of (x-x^2)/(sqrt(x))

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

integral of (5x-15)/((x^2+2x+4)^2)

\int \frac{5 x - 15}{( x ^{2} + 2 x + 4 ) ^{2}} d x

integral of x^2((1-x)-((1-x)^2)/2)

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

integral of x(1+x)^4

\int x (1 + x)^{4} d x

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

\int \frac{3 x + 5}{x ^{2} - 3 x + 2} d x

Frequently Asked Questions (FAQ)

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