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

The integral of 2sqrt(t)+3 is 4/3 t^{3/2}+3t+C

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integral of 2sqrt(t)+3

\int 2 t + 3 d t

\frac{4}{3} t^{\frac{3}{2}} + 3 t + C

Solution steps

\int 2 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 2 t d t + \int 3 d t

\int 2 t d t = \frac{4}{3} t^{\frac{3}{2}}

\int 3 d t = 3 t

= \frac{4}{3} t^{\frac{3}{2}} + 3 t

Add a constant to the solution

= \frac{4}{3} t^{\frac{3}{2}} + 3 t + C

What is the integral of 2sqrt(t)+3 ?
The integral of 2sqrt(t)+3 is 4/3 t^{3/2}+3t+C