3.1896 \(\int (2 x+5 x^2) \, dx\)

Optimal. Leaf size=11 \[ \frac{5 x^3}{3}+x^2 \]

[Out]

x^2 + (5*x^3)/3

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Rubi [A]  time = 0.0014909, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{5 x^3}{3}+x^2 \]

Antiderivative was successfully verified.

[In]

Int[2*x + 5*x^2,x]

[Out]

x^2 + (5*x^3)/3

Rubi steps

\begin{align*} \int \left (2 x+5 x^2\right ) \, dx &=x^2+\frac{5 x^3}{3}\\ \end{align*}

Mathematica [A]  time = 0.0000475, size = 11, normalized size = 1. \[ \frac{5 x^3}{3}+x^2 \]

Antiderivative was successfully verified.

[In]

Integrate[2*x + 5*x^2,x]

[Out]

x^2 + (5*x^3)/3

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Maple [A]  time = 0.001, size = 10, normalized size = 0.9 \begin{align*}{x}^{2}+{\frac{5\,{x}^{3}}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5*x^2+2*x,x)

[Out]

x^2+5/3*x^3

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Maxima [A]  time = 0.969249, size = 12, normalized size = 1.09 \begin{align*} \frac{5}{3} \, x^{3} + x^{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^2+2*x,x, algorithm="maxima")

[Out]

5/3*x^3 + x^2

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Fricas [A]  time = 1.9637, size = 20, normalized size = 1.82 \begin{align*} \frac{5}{3} x^{3} + x^{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^2+2*x,x, algorithm="fricas")

[Out]

5/3*x^3 + x^2

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Sympy [A]  time = 0.048115, size = 8, normalized size = 0.73 \begin{align*} \frac{5 x^{3}}{3} + x^{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x**2+2*x,x)

[Out]

5*x**3/3 + x**2

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Giac [A]  time = 1.05408, size = 12, normalized size = 1.09 \begin{align*} \frac{5}{3} \, x^{3} + x^{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^2+2*x,x, algorithm="giac")

[Out]

5/3*x^3 + x^2