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 (4 t + 2)^{2} d t

f (x) = cos (x), sin (x), 0, \frac{2 π}{4}

\int x^{6} sin (4 x) d x

f (x) = x + x

(t^{- 1})^{^{'}}

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