What is the integral from 0 to x of (2t^2+sqrt(t)) ?

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

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integral from 0 to x of (2t^2+sqrt(t))

\int_{0}^{x} (2 t^{2} + t) d t

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

Solution steps

\int_{0}^{x} 2 t^{2} + 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} 2 t^{2} d t + \int_{0}^{x} t d t

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

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

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

x \to \infty lim (x_{1})

\int (8 - x) d x

f (x) = x^{2} - 1

7 x - x^{2}, 2 x, (0, 10)

x (4 x - 12)^{3}

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