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

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

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integral of x^2+sqrt(x)

\int x^{2} + x d x

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

Solution steps

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

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

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

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

Add a constant to the solution

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

2 y^{^{''}} + 3 y^{^{'}} - 4 y = 5 e^{3 x}

n = 1 \sum \infty \frac{( 3 x - 2 ) ^{n}}{n}

\frac{d}{d x} (x^{3} e^{- \frac{3}{x}})

n = 1 \sum \infty \frac{7 n}{5 n + 1}

\int 20 x sec^{2} (x) d x

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