What is the integral of 3x^2-sqrt(5x)+2 ?

The integral of 3x^2-sqrt(5x)+2 is x^3-sqrt(5) 2/3 x^{3/2}+2x+C

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integral of 3x^2-sqrt(5x)+2

\int 3 x^{2} - 5 x + 2 d x

x^{3} - 5 \frac{2}{3} x^{\frac{3}{2}} + 2 x + C

Solution steps

\int 3 x^{2} - 5 x + 2 d x

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \int 3 x^{2} - 5 x + 2 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^{2} d x - \int 5 x d x + \int 2 d x

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

\int 5 x d x = 5 \frac{2}{3} x^{\frac{3}{2}}

\int 2 d x = 2 x

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

Add a constant to the solution

= x^{3} - 5 \frac{2}{3} x^{\frac{3}{2}} + 2 x + C

\int_{0}^{\infty} 6 e^{- 3 x} d x

\frac{d}{d x} (\frac{x - 19}{x - 19})

f (x) = x^{4} - 13 x^{2} + 36, at x = 1

(25 t) ((\frac{t}{25})^{2})

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

What is the integral of 3x^2-sqrt(5x)+2 ?
The integral of 3x^2-sqrt(5x)+2 is x^3-sqrt(5) 2/3 x^{3/2}+2x+C