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

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

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

\int (3 t^{2} - 5 t + 2) d t

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

Solution steps

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

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

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 t^{2} d t - \int 5 t d t + \int 2 d t

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

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

\int 2 d t = 2 t

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

Add a constant to the solution

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

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