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

x \to - 2 + lim (\frac{x - 1}{x ^{2} - 4})

f (x) = \frac{7 x ^{2} - x + 9}{6 - 7 x}

\int x (\frac{1}{1 - x ^{2}}) d x

2 (3 x^{2} ln (10 x) + x^{2})

\int (- x^{3} - 8 x + 5) 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