3.47.70 \(\int (-24 x+(48+24 x) \log (2)) \, dx\)

Optimal. Leaf size=16 \[ 12 (4+x) (4+3 x+x (-4+\log (2))) \]

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Rubi [A]  time = 0.00, antiderivative size = 15, normalized size of antiderivative = 0.94, 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*} 12 (x+2)^2 \log (2)-12 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-24*x + (48 + 24*x)*Log[2],x]

[Out]

-12*x^2 + 12*(2 + x)^2*Log[2]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-12 x^2+12 (2+x)^2 \log (2)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 23, normalized size = 1.44 \begin {gather*} 24 \left (-\frac {x^2}{2}+\frac {1}{2} x^2 \log (2)+x \log (4)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-24*x + (48 + 24*x)*Log[2],x]

[Out]

24*(-1/2*x^2 + (x^2*Log[2])/2 + x*Log[4])

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fricas [A]  time = 0.53, size = 17, normalized size = 1.06 \begin {gather*} -12 \, x^{2} + 12 \, {\left (x^{2} + 4 \, x\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x+48)*log(2)-24*x,x, algorithm="fricas")

[Out]

-12*x^2 + 12*(x^2 + 4*x)*log(2)

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giac [A]  time = 0.20, size = 17, normalized size = 1.06 \begin {gather*} -12 \, x^{2} + 12 \, {\left (x^{2} + 4 \, x\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x+48)*log(2)-24*x,x, algorithm="giac")

[Out]

-12*x^2 + 12*(x^2 + 4*x)*log(2)

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maple [A]  time = 0.02, size = 16, normalized size = 1.00

method	result	size
gosper	\(12 x \left (x \ln \relax (2)+4 \ln \relax (2)-x \right )\)	\(16\)
norman	\(\left (12 \ln \relax (2)-12\right ) x^{2}+48 x \ln \relax (2)\)	\(17\)
default	\(\ln \relax (2) \left (12 x^{2}+48 x \right )-12 x^{2}\)	\(19\)
risch	\(12 x^{2} \ln \relax (2)+48 x \ln \relax (2)-12 x^{2}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((24*x+48)*ln(2)-24*x,x,method=_RETURNVERBOSE)

[Out]

12*x*(x*ln(2)+4*ln(2)-x)

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maxima [A]  time = 0.36, size = 17, normalized size = 1.06 \begin {gather*} -12 \, x^{2} + 12 \, {\left (x^{2} + 4 \, x\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x+48)*log(2)-24*x,x, algorithm="maxima")

[Out]

-12*x^2 + 12*(x^2 + 4*x)*log(2)

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mupad [B]  time = 0.03, size = 16, normalized size = 1.00 \begin {gather*} \left (12\,\ln \relax (2)-12\right )\,x^2+48\,\ln \relax (2)\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(2)*(24*x + 48) - 24*x,x)

[Out]

48*x*log(2) + x^2*(12*log(2) - 12)

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sympy [A]  time = 0.05, size = 15, normalized size = 0.94 \begin {gather*} x^{2} \left (-12 + 12 \log {\relax (2 )}\right ) + 48 x \log {\relax (2 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x+48)*ln(2)-24*x,x)

[Out]

x**2*(-12 + 12*log(2)) + 48*x*log(2)

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