3.94.96 \(\int (-6+2 x+6 x^2 \log (16)) \, dx\)

Optimal. Leaf size=16 \[ 5+(3-x)^2+2 x^3 \log (16) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.88, number of steps used = 1, number of rules used = 0, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 2 x^3 \log (16)+x^2-6 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-6 + 2*x + 6*x^2*Log[16],x]

[Out]

-6*x + x^2 + 2*x^3*Log[16]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-6 x+x^2+2 x^3 \log (16)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.88 \begin {gather*} -6 x+x^2+2 x^3 \log (16) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-6 + 2*x + 6*x^2*Log[16],x]

[Out]

-6*x + x^2 + 2*x^3*Log[16]

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fricas [A]  time = 1.15, size = 14, normalized size = 0.88 \begin {gather*} 8 \, x^{3} \log \relax (2) + x^{2} - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(24*x^2*log(2)+2*x-6,x, algorithm="fricas")

[Out]

8*x^3*log(2) + x^2 - 6*x

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giac [A]  time = 0.15, size = 14, normalized size = 0.88 \begin {gather*} 8 \, x^{3} \log \relax (2) + x^{2} - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(24*x^2*log(2)+2*x-6,x, algorithm="giac")

[Out]

8*x^3*log(2) + x^2 - 6*x

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maple [A]  time = 0.03, size = 13, normalized size = 0.81

method	result	size
gosper	\(x \left (8 x^{2} \ln \relax (2)+x -6\right )\)	\(13\)
default	\(8 x^{3} \ln \relax (2)+x^{2}-6 x\)	\(15\)
norman	\(8 x^{3} \ln \relax (2)+x^{2}-6 x\)	\(15\)
risch	\(8 x^{3} \ln \relax (2)+x^{2}-6 x\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(24*x^2*ln(2)+2*x-6,x,method=_RETURNVERBOSE)

[Out]

x*(8*x^2*ln(2)+x-6)

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maxima [A]  time = 0.34, size = 14, normalized size = 0.88 \begin {gather*} 8 \, x^{3} \log \relax (2) + x^{2} - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(24*x^2*log(2)+2*x-6,x, algorithm="maxima")

[Out]

8*x^3*log(2) + x^2 - 6*x

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mupad [B]  time = 0.03, size = 12, normalized size = 0.75 \begin {gather*} x\,\left (8\,\ln \relax (2)\,x^2+x-6\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + 24*x^2*log(2) - 6,x)

[Out]

x*(x + 8*x^2*log(2) - 6)

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sympy [A]  time = 0.05, size = 14, normalized size = 0.88 \begin {gather*} 8 x^{3} \log {\relax (2 )} + x^{2} - 6 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(24*x**2*ln(2)+2*x-6,x)

[Out]

8*x**3*log(2) + x**2 - 6*x

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