What is the integral of (-3sqrt(x)+2x) ?

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

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integral of (-3sqrt(x)+2x)

\int (- 3 x + 2 x) d x

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

Solution steps

\int - 3 x + 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 3 x d x + \int 2 x d x

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

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

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

Add a constant to the solution

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

\int_{2}^{5} (2 - x) (x - 5) d x

\frac{\partial}{\partial x} (1 - \frac{5}{y} + x)

x (3 x - 4)

\int \frac{2}{1 + x ^{2} + y ^{2}} d y

\frac{d}{d x} (\frac{3 x}{4})

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