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

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

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integral of 3x-sqrt(x)

\int 3 x - x d x

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

Solution steps

\int 3 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

= \int 3 x d x - \int x d x

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

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

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

Add a constant to the solution

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

\int_{1}^{4} \int_{1}^{x} 2 y e^{- x} d y d x

\int x (x^{2} + 3)^{12} d x

\frac{\partial}{\partial y} (x^{2} - 3 x y)

30 y^{^{''}} - 25 y^{^{'}} = 0

\int x e^{x} d x

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