What is the integral of ((sqrt(x)-b)^2)/(sqrt(x)) ?

The integral of ((sqrt(x)-b)^2)/(sqrt(x)) is 2/3 x^{3/2}-2bx+2b^2sqrt(x)+C

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integral of ((sqrt(x)-b)^2)/(sqrt(x))

\int \frac{( x - b ) ^{2}}{x} d x

\frac{2}{3} x^{\frac{3}{2}} - 2 b x + 2 b^{2} x + C

Solution steps

\int \frac{( x - b ) ^{2}}{x} d x

Expand

\frac{( x - b ) ^{2}}{x} : x - 2 b + \frac{b ^{2}}{x}

= \int x - 2 b + \frac{b ^{2}}{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 x d x - \int 2 b d x + \int \frac{b ^{2}}{x} d x

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

\int 2 b d x = 2 b x

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

= \frac{2}{3} x^{\frac{3}{2}} - 2 b x + 2 b^{2} x

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} - 2 b x + 2 b^{2} x + C

\int_{- 1}^{1} (x + 1)^{2} d x

\int 700 x 3 + 2 x d x

\int_{0}^{2} x^{3} d x

\int_{1}^{3} \frac{7}{x ^{2}} d x

\frac{d}{d t} (y + v (t) \cdot t + (\frac{a}{2}) \cdot t^{2})

What is the integral of ((sqrt(x)-b)^2)/(sqrt(x)) ?
The integral of ((sqrt(x)-b)^2)/(sqrt(x)) is 2/3 x^{3/2}-2bx+2b^2sqrt(x)+C