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

Optimal. Leaf size=14 \[ x^3 \left (x+\left (1+\frac {1}{x}\right ) \log (2)\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.14, number of steps used = 2, number of rules used = 0, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^4+x^3 \log (2)+x^2 \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[4*x^3 + (2*x + 3*x^2)*Log[2],x]

[Out]

x^4 + x^2*Log[2] + x^3*Log[2]

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 22, normalized size = 1.57 \begin {gather*} x^4+\frac {1}{2} x^2 \log (4)+\frac {1}{3} x^3 \log (8) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

x^4 + (x^2*Log[4])/2 + (x^3*Log[8])/3

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fricas [A]  time = 0.63, size = 14, normalized size = 1.00 \begin {gather*} x^{4} + {\left (x^{3} + x^{2}\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^4 + (x^3 + x^2)*log(2)

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giac [A]  time = 0.28, size = 14, normalized size = 1.00 \begin {gather*} x^{4} + {\left (x^{3} + x^{2}\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^4 + (x^3 + x^2)*log(2)

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maple [A]  time = 0.02, size = 15, normalized size = 1.07

method	result	size
gosper	\(x^{2} \left (x \ln \relax (2)+x^{2}+\ln \relax (2)\right )\)	\(15\)
default	\(\left (x^{3}+x^{2}\right ) \ln \relax (2)+x^{4}\)	\(15\)
norman	\(x^{4}+x^{3} \ln \relax (2)+x^{2} \ln \relax (2)\)	\(17\)
risch	\(x^{4}+x^{3} \ln \relax (2)+x^{2} \ln \relax (2)\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.53, size = 14, normalized size = 1.00 \begin {gather*} x^{4} + {\left (x^{3} + x^{2}\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^4 + (x^3 + x^2)*log(2)

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mupad [B]  time = 0.04, size = 14, normalized size = 1.00 \begin {gather*} x^2\,\left (x^2+\ln \relax (2)\,x+\ln \relax (2)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(2)*(2*x + 3*x^2) + 4*x^3,x)

[Out]

x^2*(log(2) + x*log(2) + x^2)

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sympy [A]  time = 0.06, size = 15, normalized size = 1.07 \begin {gather*} x^{4} + x^{3} \log {\relax (2 )} + x^{2} \log {\relax (2 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**4 + x**3*log(2) + x**2*log(2)

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