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Popular >

integral of (x-1/x)

Solution

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

Solution

\frac{x ^{2}}{2} - ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{2}}{2} - ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} - ln ∣ x ∣ + C

Popular Examples

derivative of (x+1)/(x+3)derivative of

\frac{x + 1}{x + 3}

y^{''}-3y^'+2y=e^t

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{t}

integral of 4xln(3x)

\int 4 x ln (3 x) d x

((dy)/(dx))-(y/(3x))+(x/(3y))=0

(\frac{d y}{d x}) - (\frac{y}{3 x}) + (\frac{x}{3 y}) = 0

integral of ye^{ty}

\int y e^{t y}

Frequently Asked Questions (FAQ)

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