3.19.96 \(\int (2 x+5 x^2) \, dx\) [1896]

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

[Out]

x^2+5/3*x^3

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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {5 x^3}{3}+x^2 \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} x^2+\frac {5 x^3}{3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*x + 5*x^2,x]

[Out]

x^2 + (5*x^3)/3

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Mathics [A]
time = 1.65, size = 10, normalized size = 0.91 \begin {gather*} \frac {x^2 \left (3+5 x\right )}{3} \end {gather*}

Antiderivative was successfully verified.

[In]

mathics('Integrate[2*x + 5*x^2,x]')

[Out]

x ^ 2 (3 + 5 x) / 3

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Maple [A]
time = 0.01, size = 10, normalized size = 0.91

method	result	size
default	\(x^{2}+\frac {5}{3} x^{3}\)	\(10\)
norman	\(x^{2}+\frac {5}{3} x^{3}\)	\(10\)
risch	\(x^{2}+\frac {5}{3} x^{3}\)	\(10\)
gosper	\(\frac {x^{2} \left (3+5 x \right )}{3}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5*x^2+2*x,x,method=_RETURNVERBOSE)

[Out]

x^2+5/3*x^3

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Maxima [A]
time = 0.26, size = 9, normalized size = 0.82 \begin {gather*} \frac {5}{3} \, x^{3} + x^{2} \end {gather*}

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 = 0.29, size = 9, normalized size = 0.82 \begin {gather*} \frac {5}{3} \, x^{3} + x^{2} \end {gather*}

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 = 0.03, size = 8, normalized size = 0.73 \begin {gather*} \frac {5 x^{3}}{3} + x^{2} \end {gather*}

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 = 0.00, size = 15, normalized size = 1.36 \begin {gather*} \frac {5}{3} x^{3}+\frac {2}{2} x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5/3*x^3 + x^2

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Mupad [B]
time = 0.02, size = 10, normalized size = 0.91 \begin {gather*} \frac {x^2\,\left (5\,x+3\right )}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + 5*x^2,x)

[Out]

(x^2*(5*x + 3))/3

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