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Popular >

integral of (2x-1/x)

Solution

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

Solution

x^{2} - ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= x^{2} - ln ∣ x ∣

Add a constant to the solution

= x^{2} - ln ∣ x ∣ + C

Graph

Popular Examples

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

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

integral of (sqrt(x-1))/(3x)

\int \frac{x - 1}{3 x} d x

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\int (cos^{2} (4 x)) d x

integral of-x^5e^{x^6}

\int - x^{5} e^{x^{6}} d x

integral of tsin^2(2t)

\int t sin^{2} (2 t) d t

Frequently Asked Questions (FAQ)

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