What is the integral of 2-4t+5t^{3/2} ?

The integral of 2-4t+5t^{3/2} is 2t-2t^2+2t^{5/2}+C

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integral of 2-4t+5t^{3/2}

\int 2 - 4 t + 5 t^{\frac{3}{2}} d t

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

Solution steps

\int 2 - 4 t + 5 t^{\frac{3}{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 2 d t - \int 4 t d t + \int 5 t^{\frac{3}{2}} d t

\int 2 d t = 2 t

\int 4 t d t = 2 t^{2}

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

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

Add a constant to the solution

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

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What is the integral of 2-4t+5t^{3/2} ?
The integral of 2-4t+5t^{3/2} is 2t-2t^2+2t^{5/2}+C