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Popular >

integral of-1/x+c

Solution

\int - \frac{1}{x} + c d x

Solution

- ln ∣ x ∣ + c x + C

Solution steps

\int - \frac{1}{x} + c 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 \frac{1}{x} d x + \int c d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int c d x = c x

= - ln ∣ x ∣ + c x

Add a constant to the solution

= - ln ∣ x ∣ + c x + C

Popular Examples

tangent of f(x)=-7x^2+3x,\at x=4 tangent of

f (x) = - 7 x^{2} + 3 x, at x = 4

limit as x approaches 2 of x^2-2x

x \to 2 lim (x^{2} - 2 x)

4x^2y^{''}+8xy^'-3y=0

4 x^{2} y^{^{''}} + 8 x y^{^{'}} - 3 y = 0

limit as x approaches 0-of (sin(x))/x

x \to 0 - lim (\frac{sin ( x )}{x})

derivative of sin(x-cos^2(x))

\frac{d}{d x} (sin (x) - cos^{2} (x))

Frequently Asked Questions (FAQ)

What is the integral of-1/x+c ?
The integral of-1/x+c is -ln|x|+cx+C