What is the integral from 0 to x of (1+sqrt(t)) ?

The integral from 0 to x of (1+sqrt(t)) is x+(2x^{3/2})/3

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integral from 0 to x of (1+sqrt(t))

\int_{0}^{x} (1 + t) d t

x + \frac{2 x ^{\frac{3}{2}}}{3}

Solution steps

\int_{0}^{x} 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

= \int_{0}^{x} 1 d t + \int_{0}^{x} t d t

\int_{0}^{x} 1 d t = x

\int_{0}^{x} t d t = \frac{2 x ^{\frac{3}{2}}}{3}

= x + \frac{2 x ^{\frac{3}{2}}}{3}

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What is the integral from 0 to x of (1+sqrt(t)) ?
The integral from 0 to x of (1+sqrt(t)) is x+(2x^{3/2})/3