3.99.37 \(\int (3 x^2+x^4+5 x^4 \log (x)) \, dx\)

Optimal. Leaf size=17 \[ x \left (\frac {2}{x}+x^2+x^4 \log (x)\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 10, normalized size of antiderivative = 0.59, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2304} \begin {gather*} x^5 \log (x)+x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3*x^2 + x^4 + 5*x^4*Log[x],x]

[Out]

x^3 + x^5*Log[x]

Rule 2304

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log[c*x^
n]))/(d*(m + 1)), x] - Simp[(b*n*(d*x)^(m + 1))/(d*(m + 1)^2), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x^3+\frac {x^5}{5}+5 \int x^4 \log (x) \, dx\\ &=x^3+x^5 \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.59 \begin {gather*} x^3+x^5 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3*x^2 + x^4 + 5*x^4*Log[x],x]

[Out]

x^3 + x^5*Log[x]

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fricas [A]  time = 0.75, size = 10, normalized size = 0.59 \begin {gather*} x^{5} \log \relax (x) + x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^4*log(x)+x^4+3*x^2,x, algorithm="fricas")

[Out]

x^5*log(x) + x^3

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giac [A]  time = 0.23, size = 10, normalized size = 0.59 \begin {gather*} x^{5} \log \relax (x) + x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^4*log(x)+x^4+3*x^2,x, algorithm="giac")

[Out]

x^5*log(x) + x^3

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maple [A]  time = 0.02, size = 11, normalized size = 0.65

method	result	size
default	\(x^{3}+x^{5} \ln \relax (x )\)	\(11\)
norman	\(x^{3}+x^{5} \ln \relax (x )\)	\(11\)
risch	\(x^{3}+x^{5} \ln \relax (x )\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5*x^4*ln(x)+x^4+3*x^2,x,method=_RETURNVERBOSE)

[Out]

x^3+x^5*ln(x)

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maxima [A]  time = 0.34, size = 10, normalized size = 0.59 \begin {gather*} x^{5} \log \relax (x) + x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^4*log(x)+x^4+3*x^2,x, algorithm="maxima")

[Out]

x^5*log(x) + x^3

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mupad [B]  time = 5.89, size = 10, normalized size = 0.59 \begin {gather*} x^5\,\ln \relax (x)+x^3 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5*x^4*log(x) + 3*x^2 + x^4,x)

[Out]

x^5*log(x) + x^3

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sympy [A]  time = 0.09, size = 8, normalized size = 0.47 \begin {gather*} x^{5} \log {\relax (x )} + x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x**4*ln(x)+x**4+3*x**2,x)

[Out]

x**5*log(x) + x**3

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