What is the integral of (2x+5-1/x) ?

The integral of (2x+5-1/x) is x^2+5x-ln|x|+C

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integral of (2x+5-1/x)

\int (2 x + 5 - \frac{1}{x}) d x

x^{2} + 5 x - ln ∣ x ∣ + C

Solution steps

\int 2 x + 5 - \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 5 d x - \int \frac{1}{x} d x

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

\int 5 d x = 5 x

\int \frac{1}{x} d x = ln ∣ x ∣

= x^{2} + 5 x - ln ∣ x ∣

Add a constant to the solution

= x^{2} + 5 x - ln ∣ x ∣ + C

\frac{\partial}{\partial y} (6 x y)

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

\frac{d}{d x} (\frac{x ^{3} - 2}{x})

y^{^{'}} = \frac{y ^{2} - x ^{2}}{x y}

3 x^{2} + \frac{8 x}{3} - 2

What is the integral of (2x+5-1/x) ?
The integral of (2x+5-1/x) is x^2+5x-ln|x|+C