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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

Popular Examples

integral of cos^5(x)sin^5(x)

\int cos^{5} (x) sin^{5} (x) d x

integral of (10)/(x^2-25)

\int \frac{10}{x ^{2} - 25} d x

integral of arctan(1+sqrt(x))

\int arctan (1 + x) d x

integral of 7x(x^2+8)^2

\int 7 x (x^{2} + 8)^{2} d x

integral of r/((5-4r-r^2)^{3/2)}

\int \frac{r}{( 5 - 4 r - r ^{2} ) ^{\frac{3}{2}}} d r

Frequently Asked Questions (FAQ)

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