What is the integral of 2x^2+sqrt(x) ?

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

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integral of 2x^2+sqrt(x)

\int 2 x^{2} + x d x

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

Solution steps

\int 2 x^{2} + x d x

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 x^{2} d x + \int x d x

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (11 arctan (x))

x \to 5 + lim (\frac{( x + 1 )}{x - 5})

3 x^{2} - 2 x

\int \frac{s}{s ^{2} + 3 s + 6} d s

x = - 2 y^{2} + 3 y - 5, x + 3 y = - 13

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