What is the integral of (5(x-3)^2)/(xsqrt(x)) ?

The integral of (5(x-3)^2)/(xsqrt(x)) is 5(2/3 x^{3/2}-12sqrt(x)-(18)/(sqrt(x)))+C

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integral of (5(x-3)^2)/(xsqrt(x))

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

5 (\frac{2}{3} x^{\frac{3}{2}} - 12 x - \frac{18}{x}) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int \frac{( x - 3 ) ^{2}}{x x} d x

Expand

\frac{( x - 3 ) ^{2}}{x x} : x - \frac{6}{x} + \frac{9}{x x}

= 5 \cdot \int x - \frac{6}{x} + \frac{9}{x 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

= 5 (\int x d x - \int \frac{6}{x} d x + \int \frac{9}{x x} d x)

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

\int \frac{6}{x} d x = 12 x

\int \frac{9}{x x} d x = - \frac{18}{x}

= 5 (\frac{2}{3} x^{\frac{3}{2}} - 12 x - \frac{18}{x})

Add a constant to the solution

= 5 (\frac{2}{3} x^{\frac{3}{2}} - 12 x - \frac{18}{x}) + C

f (x) = \frac{3}{5} x^{15}

\int_{0}^{2} \frac{y}{25 - y ^{2}} d y

x \to - \infty lim (\frac{x ^{6} + cos ( x ^{10000} )}{x + 5})

f (x) = x^{11}

\frac{( x ^{2} )}{5 + 6 x}

What is the integral of (5(x-3)^2)/(xsqrt(x)) ?
The integral of (5(x-3)^2)/(xsqrt(x)) is 5(2/3 x^{3/2}-12sqrt(x)-(18)/(sqrt(x)))+C