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

Optimal. Leaf size=10 \[ \left (-5+x^3\right ) (x+\log (4)) \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.30, number of steps used = 1, number of rules used = 0, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^4+x^3 \log (4)-5 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-5 + 4*x^3 + 3*x^2*Log[4],x]

[Out]

-5*x + x^4 + x^3*Log[4]

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.30 \begin {gather*} -5 x+x^4+x^3 \log (4) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-5*x + x^4 + x^3*Log[4]

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fricas [A]  time = 0.55, size = 14, normalized size = 1.40 \begin {gather*} x^{4} + 2 \, x^{3} \log \relax (2) - 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x^2*log(2)+4*x^3-5,x, algorithm="fricas")

[Out]

x^4 + 2*x^3*log(2) - 5*x

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giac [A]  time = 0.26, size = 14, normalized size = 1.40 \begin {gather*} x^{4} + 2 \, x^{3} \log \relax (2) - 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x^2*log(2)+4*x^3-5,x, algorithm="giac")

[Out]

x^4 + 2*x^3*log(2) - 5*x

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maple [A]  time = 0.04, size = 15, normalized size = 1.50

method	result	size
gosper	\(x^{4}+2 x^{3} \ln \relax (2)-5 x\)	\(15\)
default	\(x^{4}+2 x^{3} \ln \relax (2)-5 x\)	\(15\)
norman	\(x^{4}+2 x^{3} \ln \relax (2)-5 x\)	\(15\)
risch	\(x^{4}+2 x^{3} \ln \relax (2)-5 x\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x^2*ln(2)+4*x^3-5,x,method=_RETURNVERBOSE)

[Out]

x^4+2*x^3*ln(2)-5*x

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maxima [A]  time = 0.62, size = 14, normalized size = 1.40 \begin {gather*} x^{4} + 2 \, x^{3} \log \relax (2) - 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x^2*log(2)+4*x^3-5,x, algorithm="maxima")

[Out]

x^4 + 2*x^3*log(2) - 5*x

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mupad [B]  time = 0.03, size = 14, normalized size = 1.40 \begin {gather*} x^4+2\,\ln \relax (2)\,x^3-5\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x^2*log(2) + 4*x^3 - 5,x)

[Out]

2*x^3*log(2) - 5*x + x^4

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sympy [A]  time = 0.05, size = 14, normalized size = 1.40 \begin {gather*} x^{4} + 2 x^{3} \log {\relax (2 )} - 5 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x**2*ln(2)+4*x**3-5,x)

[Out]

x**4 + 2*x**3*log(2) - 5*x

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