What is the integral of 30(1+sqrt(t)) ?

The integral of 30(1+sqrt(t)) is 30(t+2/3 t^{3/2})+C

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integral of 30(1+sqrt(t))

\int 30 (1 + t) d t

30 (t + \frac{2}{3} t^{\frac{3}{2}}) + C

Solution steps

\int 30 (1 + t) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 30 \cdot \int 1 + t 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

= 30 (\int 1 d t + \int t d t)

\int 1 d t = t

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

= 30 (t + \frac{2}{3} t^{\frac{3}{2}})

Add a constant to the solution

= 30 (t + \frac{2}{3} t^{\frac{3}{2}}) + C

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n = 0 \sum \infty \frac{( - 1 ) ^{n} 7 ^{n} x ^{n}}{5 ^{n + 1}}

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What is the integral of 30(1+sqrt(t)) ?
The integral of 30(1+sqrt(t)) is 30(t+2/3 t^{3/2})+C