3.70.24 \(\int \frac {390625+781250 x+12 x^{11} \log ^4(9)}{390625} \, dx\)

Optimal. Leaf size=17 \[ 1+x+x^2+\frac {x^{12} \log ^4(9)}{390625} \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {12} \begin {gather*} \frac {x^{12} \log ^4(9)}{390625}+x^2+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(390625 + 781250*x + 12*x^11*Log[9]^4)/390625,x]

[Out]

x + x^2 + (x^12*Log[9]^4)/390625

Rule 12

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (390625+781250 x+12 x^{11} \log ^4(9)\right ) \, dx}{390625}\\ &=x+x^2+\frac {x^{12} \log ^4(9)}{390625}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.94 \begin {gather*} x+x^2+\frac {x^{12} \log ^4(9)}{390625} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(390625 + 781250*x + 12*x^11*Log[9]^4)/390625,x]

[Out]

x + x^2 + (x^12*Log[9]^4)/390625

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fricas [A]  time = 0.57, size = 14, normalized size = 0.82 \begin {gather*} \frac {16}{390625} \, x^{12} \log \relax (3)^{4} + x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(192/390625*x^11*log(3)^4+2*x+1,x, algorithm="fricas")

[Out]

16/390625*x^12*log(3)^4 + x^2 + x

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giac [A]  time = 0.15, size = 14, normalized size = 0.82 \begin {gather*} \frac {16}{390625} \, x^{12} \log \relax (3)^{4} + x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(192/390625*x^11*log(3)^4+2*x+1,x, algorithm="giac")

[Out]

16/390625*x^12*log(3)^4 + x^2 + x

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maple [A]  time = 0.03, size = 15, normalized size = 0.88

method	result	size
default	\(\frac {16 x^{12} \ln \relax (3)^{4}}{390625}+x^{2}+x\)	\(15\)
norman	\(\frac {16 x^{12} \ln \relax (3)^{4}}{390625}+x^{2}+x\)	\(15\)
risch	\(\frac {16 x^{12} \ln \relax (3)^{4}}{390625}+x^{2}+x\)	\(15\)
gosper	\(\frac {x \left (16 x^{11} \ln \relax (3)^{4}+390625 x +390625\right )}{390625}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(192/390625*x^11*ln(3)^4+2*x+1,x,method=_RETURNVERBOSE)

[Out]

16/390625*x^12*ln(3)^4+x^2+x

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maxima [A]  time = 0.36, size = 14, normalized size = 0.82 \begin {gather*} \frac {16}{390625} \, x^{12} \log \relax (3)^{4} + x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(192/390625*x^11*log(3)^4+2*x+1,x, algorithm="maxima")

[Out]

16/390625*x^12*log(3)^4 + x^2 + x

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mupad [B]  time = 0.03, size = 14, normalized size = 0.82 \begin {gather*} \frac {16\,{\ln \relax (3)}^4\,x^{12}}{390625}+x^2+x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + (192*x^11*log(3)^4)/390625 + 1,x)

[Out]

x + (16*x^12*log(3)^4)/390625 + x^2

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sympy [A]  time = 0.05, size = 15, normalized size = 0.88 \begin {gather*} \frac {16 x^{12} \log {\relax (3 )}^{4}}{390625} + x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(192/390625*x**11*ln(3)**4+2*x+1,x)

[Out]

16*x**12*log(3)**4/390625 + x**2 + x

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