What is the integral of x^3+3x^2-2sqrt(x) ?

The integral of x^3+3x^2-2sqrt(x) is (x^4)/4+x^3-4/3 x^{3/2}+C

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integral of x^3+3x^2-2sqrt(x)

\int x^{3} + 3 x^{2} - 2 x d x

\frac{x ^{4}}{4} + x^{3} - \frac{4}{3} x^{\frac{3}{2}} + C

Solution steps

\int x^{3} + 3 x^{2} - 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^{3} d x + \int 3 x^{2} d x - \int 2 x d x

\int x^{3} d x = \frac{x ^{4}}{4}

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

\int 2 x d x = \frac{4}{3} x^{\frac{3}{2}}

= \frac{x ^{4}}{4} + x^{3} - \frac{4}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{x ^{4}}{4} + x^{3} - \frac{4}{3} x^{\frac{3}{2}} + C

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What is the integral of x^3+3x^2-2sqrt(x) ?
The integral of x^3+3x^2-2sqrt(x) is (x^4)/4+x^3-4/3 x^{3/2}+C