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

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

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

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

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

Solution steps

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

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

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

\int 3 d t = 3 t

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

Add a constant to the solution

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

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