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Popular >

integral of 1/x-x

Solution

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

Solution

ln ∣ x ∣ - \frac{x ^{2}}{2} + C

Solution steps

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - \frac{x ^{2}}{2}

Add a constant to the solution

= ln ∣ x ∣ - \frac{x ^{2}}{2} + C

Popular Examples

tangent of y= 3/x ,(-2,-3/2)tangent of

y = \frac{3}{x}, (- 2, - \frac{3}{2})

integral of x^{1/9}

\int x^{\frac{1}{9}} d x

integral of (x+1)sec(x^2+2x)tan(x^2+2x)

\int (x + 1) sec (x^{2} + 2 x) tan (x^{2} + 2 x) d x

derivative of sin^3(5x)derivative of

sin^{3} (5 x)

limit as y approaches-3 of 4y^2+4y+1

y \to - 3 lim (4 y^{2} + 4 y + 1)

Frequently Asked Questions (FAQ)

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