What is the integral of (2xsqrt(x)-1/(sqrt(x))) ?

The integral of (2xsqrt(x)-1/(sqrt(x))) is 4/5 x^{5/2}-2sqrt(x)+C

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integral of (2xsqrt(x)-1/(sqrt(x)))

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

\frac{4}{5} x^{\frac{5}{2}} - 2 x + C

Solution steps

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

\int 2 x x d x = \frac{4}{5} x^{\frac{5}{2}}

\int \frac{1}{x} d x = 2 x

= \frac{4}{5} x^{\frac{5}{2}} - 2 x

Add a constant to the solution

= \frac{4}{5} x^{\frac{5}{2}} - 2 x + C

3 y^{^{''}} - 11 y^{^{'}} + 10 y = 0, y (0) = 8, y^{^{'}} (0) = - 4

\int (e^{4 x} - e^{- 4 x})^{2} d x

\int \frac{5}{6} csc^{2} (\frac{x}{6}) d x

\int \frac{( 2 x + 3 )}{x + 2} d x

f (x) = \frac{2}{3 x + 1}

What is the integral of (2xsqrt(x)-1/(sqrt(x))) ?
The integral of (2xsqrt(x)-1/(sqrt(x))) is 4/5 x^{5/2}-2sqrt(x)+C