3.36.64 \(\int (4+6 x^2+\log (x)) \, dx\)

Optimal. Leaf size=17 \[ -5+e^4+x+x \left (2+2 x^2+\log (x)\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.76, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2295} \begin {gather*} 2 x^3+3 x+x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[4 + 6*x^2 + Log[x],x]

[Out]

3*x + 2*x^3 + x*Log[x]

Rule 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.76 \begin {gather*} 3 x+2 x^3+x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[4 + 6*x^2 + Log[x],x]

[Out]

3*x + 2*x^3 + x*Log[x]

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fricas [A]  time = 0.59, size = 13, normalized size = 0.76 \begin {gather*} 2 \, x^{3} + x \log \relax (x) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)+6*x^2+4,x, algorithm="fricas")

[Out]

2*x^3 + x*log(x) + 3*x

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giac [A]  time = 0.24, size = 13, normalized size = 0.76 \begin {gather*} 2 \, x^{3} + x \log \relax (x) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)+6*x^2+4,x, algorithm="giac")

[Out]

2*x^3 + x*log(x) + 3*x

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maple [A]  time = 0.01, size = 14, normalized size = 0.82

method	result	size
default	\(2 x^{3}+3 x +x \ln \relax (x )\)	\(14\)
norman	\(2 x^{3}+3 x +x \ln \relax (x )\)	\(14\)
risch	\(2 x^{3}+3 x +x \ln \relax (x )\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(x)+6*x^2+4,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.43, size = 13, normalized size = 0.76 \begin {gather*} 2 \, x^{3} + x \log \relax (x) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)+6*x^2+4,x, algorithm="maxima")

[Out]

2*x^3 + x*log(x) + 3*x

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mupad [B]  time = 2.17, size = 11, normalized size = 0.65 \begin {gather*} x\,\left (\ln \relax (x)+2\,x^2+3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(x) + 6*x^2 + 4,x)

[Out]

x*(log(x) + 2*x^2 + 3)

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sympy [A]  time = 0.08, size = 12, normalized size = 0.71 \begin {gather*} 2 x^{3} + x \log {\relax (x )} + 3 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(x)+6*x**2+4,x)

[Out]

2*x**3 + x*log(x) + 3*x

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