3.17.18 \(\int \frac {1}{3} (15-4 \log (176)) \, dx\)

Optimal. Leaf size=12 \[ -1+5 x-\frac {4}{3} x \log (176) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.92, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {8} \begin {gather*} \frac {1}{3} x (15-4 \log (176)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(15 - 4*Log[176])/3,x]

[Out]

(x*(15 - 4*Log[176]))/3

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} x (15-4 \log (176))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} 5 x-\frac {4}{3} x \log (176) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(15 - 4*Log[176])/3,x]

[Out]

5*x - (4*x*Log[176])/3

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fricas [A]  time = 0.65, size = 9, normalized size = 0.75 \begin {gather*} -\frac {4}{3} \, x \log \left (176\right ) + 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/3*log(176)+5,x, algorithm="fricas")

[Out]

-4/3*x*log(176) + 5*x

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giac [A]  time = 0.22, size = 9, normalized size = 0.75 \begin {gather*} -\frac {1}{3} \, x {\left (4 \, \log \left (176\right ) - 15\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/3*log(176)+5,x, algorithm="giac")

[Out]

-1/3*x*(4*log(176) - 15)

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maple [A]  time = 0.02, size = 9, normalized size = 0.75

method	result	size
default	\(\left (-\frac {4 \ln \left (176\right )}{3}+5\right ) x\)	\(9\)
norman	\(\left (-\frac {4 \ln \left (176\right )}{3}+5\right ) x\)	\(9\)
risch	\(-\frac {16 x \ln \relax (2)}{3}-\frac {4 x \ln \left (11\right )}{3}+5 x\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4/3*ln(176)+5,x,method=_RETURNVERBOSE)

[Out]

(-4/3*ln(176)+5)*x

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maxima [A]  time = 0.37, size = 9, normalized size = 0.75 \begin {gather*} -\frac {1}{3} \, x {\left (4 \, \log \left (176\right ) - 15\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/3*log(176)+5,x, algorithm="maxima")

[Out]

-1/3*x*(4*log(176) - 15)

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mupad [B]  time = 0.00, size = 9, normalized size = 0.75 \begin {gather*} -x\,\left (\frac {4\,\ln \left (176\right )}{3}-5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5 - (4*log(176))/3,x)

[Out]

-x*((4*log(176))/3 - 5)

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sympy [A]  time = 0.05, size = 8, normalized size = 0.67 \begin {gather*} x \left (5 - \frac {4 \log {\left (176 \right )}}{3}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/3*ln(176)+5,x)

[Out]

x*(5 - 4*log(176)/3)

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