What is the integral of (x-1/x)sqrt(x) ?

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

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integral of (x-1/x)sqrt(x)

\int (x - \frac{1}{x}) x d x

\frac{2}{5} x^{2} x - 2 x + C

Solution steps

\int (x - \frac{1}{x}) x d x

Apply Integration By Parts

: x^{2} x - x - \int \frac{3 x ^{2} + 1}{2 x} d x

= x^{2} x - x - \int \frac{3 x ^{2} + 1}{2 x} d x

\int \frac{3 x ^{2} + 1}{2 x} d x = \frac{1}{5} x (3 x^{2} + 5)

= x^{2} x - x - \frac{1}{5} x (3 x^{2} + 5)

Simplify

x^{2} x - x - \frac{1}{5} x (3 x^{2} + 5) : \frac{2}{5} x^{2} x - 2 x

= \frac{2}{5} x^{2} x - 2 x

Add a constant to the solution

= \frac{2}{5} x^{2} x - 2 x + C

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