3.17.7 \(\int (36 x+9 x^2) \, dx\)

Optimal. Leaf size=8 \[ 3 x^2 (6+x) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.38, 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*} 3 x^3+18 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[36*x + 9*x^2,x]

[Out]

18*x^2 + 3*x^3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=18 x^2+3 x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.38 \begin {gather*} 18 x^2+3 x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[36*x + 9*x^2,x]

[Out]

18*x^2 + 3*x^3

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fricas [A]  time = 0.49, size = 11, normalized size = 1.38 \begin {gather*} 3 \, x^{3} + 18 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9*x^2+36*x,x, algorithm="fricas")

[Out]

3*x^3 + 18*x^2

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giac [A]  time = 0.22, size = 11, normalized size = 1.38 \begin {gather*} 3 \, x^{3} + 18 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9*x^2+36*x,x, algorithm="giac")

[Out]

3*x^3 + 18*x^2

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maple [A]  time = 0.01, size = 9, normalized size = 1.12

method	result	size
gosper	\(3 x^{2} \left (x +6\right )\)	\(9\)
default	\(3 x^{3}+18 x^{2}\)	\(12\)
norman	\(3 x^{3}+18 x^{2}\)	\(12\)
risch	\(3 x^{3}+18 x^{2}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(9*x^2+36*x,x,method=_RETURNVERBOSE)

[Out]

3*x^2*(x+6)

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maxima [A]  time = 0.43, size = 11, normalized size = 1.38 \begin {gather*} 3 \, x^{3} + 18 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9*x^2+36*x,x, algorithm="maxima")

[Out]

3*x^3 + 18*x^2

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mupad [B]  time = 0.02, size = 8, normalized size = 1.00 \begin {gather*} 3\,x^2\,\left (x+6\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(36*x + 9*x^2,x)

[Out]

3*x^2*(x + 6)

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sympy [A]  time = 0.05, size = 8, normalized size = 1.00 \begin {gather*} 3 x^{3} + 18 x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9*x**2+36*x,x)

[Out]

3*x**3 + 18*x**2

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