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Popular >

integral of 1-1/x

Solution

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

Solution

x - ln ∣ x ∣ + C

Solution steps

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

\int 1 d x = x

\int \frac{1}{x} d x = ln ∣ x ∣

= x - ln ∣ x ∣

Add a constant to the solution

= x - ln ∣ x ∣ + C

Popular Examples

integral of 6sin^3(xco)s^7x

\int 6 sin^{3} (x co) s^{7} x d x

integral of 1/(x^2sqrt(x^2+81))

\int \frac{1}{x ^{2} x ^{2} + 81} d x

integral from-2 to 3 of (x+3)

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

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

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

derivative of ln((5x^2+3/(x^2)))

\frac{d}{d x} (ln (\frac{5 x ^{2} + 3}{x ^{2}}))

Frequently Asked Questions (FAQ)

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