What is the integral of ((sqrt(x)-b))/(sqrt(x)) ?

The integral of ((sqrt(x)-b))/(sqrt(x)) is x-2bsqrt(x)+C

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integral of ((sqrt(x)-b))/(sqrt(x))

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

x - 2 b x + C

Solution steps

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

Expand

\frac{x - b}{x} : 1 - \frac{b}{x}

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

\int 1 d x = x

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

= x - 2 b x

Add a constant to the solution

= x - 2 b x + C

\frac{\partial}{\partial x} (sin (x) e^{y x^{2}} x)

\int \frac{z}{1 + z ^{2}} d z

\int e^{x^{2} - 2 x} d x

\frac{d}{d x} (x^{\frac{1}{2}} \cdot csc (x) sin (x))

2 y^{^{'}} - 6 x^{2} = 0

What is the integral of ((sqrt(x)-b))/(sqrt(x)) ?
The integral of ((sqrt(x)-b))/(sqrt(x)) is x-2bsqrt(x)+C