3.102.19 \(\int \frac {3 x^2}{2 \log (28)} \, dx\)

Optimal. Leaf size=11 \[ \frac {x^3}{2 \log (28)} \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 30} \begin {gather*} \frac {x^3}{2 \log (28)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3*x^2)/(2*Log[28]),x]

[Out]

x^3/(2*Log[28])

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {3 \int x^2 \, dx}{2 \log (28)}\\ &=\frac {x^3}{2 \log (28)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} \frac {x^3}{2 \log (28)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3*x^2)/(2*Log[28]),x]

[Out]

x^3/(2*Log[28])

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fricas [A]  time = 1.59, size = 9, normalized size = 0.82 \begin {gather*} \frac {x^{3}}{2 \, \log \left (28\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/2*x^2/log(28),x, algorithm="fricas")

[Out]

1/2*x^3/log(28)

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giac [A]  time = 0.16, size = 9, normalized size = 0.82 \begin {gather*} \frac {x^{3}}{2 \, \log \left (28\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/2*x^2/log(28),x, algorithm="giac")

[Out]

1/2*x^3/log(28)

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maple [A]  time = 0.03, size = 10, normalized size = 0.91

method	result	size
gosper	\(\frac {x^{3}}{2 \ln \left (28\right )}\)	\(10\)
default	\(\frac {x^{3}}{2 \ln \left (28\right )}\)	\(10\)
norman	\(\frac {x^{3}}{2 \ln \left (28\right )}\)	\(10\)
risch	\(\frac {x^{3}}{4 \ln \relax (2)+2 \ln \relax (7)}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3/2*x^2/ln(28),x,method=_RETURNVERBOSE)

[Out]

1/2*x^3/ln(28)

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maxima [A]  time = 0.34, size = 9, normalized size = 0.82 \begin {gather*} \frac {x^{3}}{2 \, \log \left (28\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/2*x^2/log(28),x, algorithm="maxima")

[Out]

1/2*x^3/log(28)

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mupad [B]  time = 0.04, size = 9, normalized size = 0.82 \begin {gather*} \frac {x^3}{2\,\ln \left (28\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x^2)/(2*log(28)),x)

[Out]

x^3/(2*log(28))

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sympy [A]  time = 0.05, size = 7, normalized size = 0.64 \begin {gather*} \frac {x^{3}}{2 \log {\left (28 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/2*x**2/ln(28),x)

[Out]

x**3/(2*log(28))

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