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

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

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integral of (2+5t^{3/2})

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

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

Solution steps

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

\int 2 d t = 2 t

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

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

Add a constant to the solution

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

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