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

\frac{d}{d x} (ln (52 x))

\frac{d y}{d x} + 9 x y = 8 x

\int_{0}^{6} \frac{π}{9} (36 - y^{2}) d y

(sin (x) - x cos (x))^{^{'}}

y^{^{'}} = 20 x y

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