3.45.94 \(\int (2 x+3 x^2) \, dx\)

Optimal. Leaf size=18 \[ 1-x^2+x^2 (2+x)-4 \log (2) \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.39, 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*} x^3+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*x + 3*x^2,x]

[Out]

x^2 + x^3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x^2+x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.39 \begin {gather*} x^2+x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*x + 3*x^2,x]

[Out]

x^2 + x^3

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fricas [A]  time = 0.60, size = 7, normalized size = 0.39 \begin {gather*} x^{3} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2+2*x,x, algorithm="fricas")

[Out]

x^3 + x^2

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giac [A]  time = 4.81, size = 7, normalized size = 0.39 \begin {gather*} x^{3} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2+2*x,x, algorithm="giac")

[Out]

x^3 + x^2

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maple [A]  time = 0.01, size = 8, normalized size = 0.44

method	result	size
gosper	\(\left (x +1\right ) x^{2}\)	\(8\)
default	\(x^{3}+x^{2}\)	\(8\)
norman	\(x^{3}+x^{2}\)	\(8\)
risch	\(x^{3}+x^{2}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2+2*x,x,method=_RETURNVERBOSE)

[Out]

(x+1)*x^2

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maxima [A]  time = 0.37, size = 7, normalized size = 0.39 \begin {gather*} x^{3} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2+2*x,x, algorithm="maxima")

[Out]

x^3 + x^2

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mupad [B]  time = 0.02, size = 7, normalized size = 0.39 \begin {gather*} x^2\,\left (x+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + 3*x^2,x)

[Out]

x^2*(x + 1)

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sympy [A]  time = 0.04, size = 5, normalized size = 0.28 \begin {gather*} x^{3} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x**2+2*x,x)

[Out]

x**3 + x**2

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