3.61.78 \(\int \frac {4 x^3}{\log ^2(2)} \, dx\)

Optimal. Leaf size=8 \[ \frac {x^4}{\log ^2(2)} \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 30} \begin {gather*} \frac {x^4}{\log ^2(2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(4*x^3)/Log[2]^2,x]

[Out]

x^4/Log[2]^2

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 {4 \int x^3 \, dx}{\log ^2(2)}\\ &=\frac {x^4}{\log ^2(2)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {x^4}{\log ^2(2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4*x^3)/Log[2]^2,x]

[Out]

x^4/Log[2]^2

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fricas [A]  time = 0.56, size = 8, normalized size = 1.00 \begin {gather*} \frac {x^{4}}{\log \relax (2)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^3/log(2)^2,x, algorithm="fricas")

[Out]

x^4/log(2)^2

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giac [A]  time = 0.14, size = 8, normalized size = 1.00 \begin {gather*} \frac {x^{4}}{\log \relax (2)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^3/log(2)^2,x, algorithm="giac")

[Out]

x^4/log(2)^2

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maple [A]  time = 0.04, size = 9, normalized size = 1.12

method	result	size
gosper	\(\frac {x^{4}}{\ln \relax (2)^{2}}\)	\(9\)
default	\(\frac {x^{4}}{\ln \relax (2)^{2}}\)	\(9\)
norman	\(\frac {x^{4}}{\ln \relax (2)^{2}}\)	\(9\)
risch	\(\frac {x^{4}}{\ln \relax (2)^{2}}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x^3/ln(2)^2,x,method=_RETURNVERBOSE)

[Out]

x^4/ln(2)^2

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maxima [A]  time = 0.33, size = 8, normalized size = 1.00 \begin {gather*} \frac {x^{4}}{\log \relax (2)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^3/log(2)^2,x, algorithm="maxima")

[Out]

x^4/log(2)^2

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mupad [B]  time = 0.03, size = 8, normalized size = 1.00 \begin {gather*} \frac {x^4}{{\ln \relax (2)}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^3)/log(2)^2,x)

[Out]

x^4/log(2)^2

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sympy [A]  time = 0.05, size = 7, normalized size = 0.88 \begin {gather*} \frac {x^{4}}{\log {\relax (2 )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x**3/ln(2)**2,x)

[Out]

x**4/log(2)**2

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