Optimal. Leaf size=47 \[ -2 a^3 b c^3 x+\frac {2}{3} a b^3 c^3 x^3-\frac {1}{4} b^4 c^3 x^4+a^4 c^3 \log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {76}
\begin {gather*} a^4 c^3 \log (x)-2 a^3 b c^3 x+\frac {2}{3} a b^3 c^3 x^3-\frac {1}{4} b^4 c^3 x^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin {align*} \int \frac {(a+b x) (a c-b c x)^3}{x} \, dx &=\int \left (-2 a^3 b c^3+\frac {a^4 c^3}{x}+2 a b^3 c^3 x^2-b^4 c^3 x^3\right ) \, dx\\ &=-2 a^3 b c^3 x+\frac {2}{3} a b^3 c^3 x^3-\frac {1}{4} b^4 c^3 x^4+a^4 c^3 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 48, normalized size = 1.02 \begin {gather*} c^3 \left (\frac {1}{12} \left (19 a^4-24 a^3 b x+8 a b^3 x^3-3 b^4 x^4\right )+a^4 \log (-b x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 36, normalized size = 0.77
method | result | size |
default | \(c^{3} \left (-\frac {b^{4} x^{4}}{4}+\frac {2 a \,b^{3} x^{3}}{3}-2 a^{3} b x +a^{4} \ln \left (x \right )\right )\) | \(36\) |
norman | \(-2 a^{3} b \,c^{3} x +\frac {2 a \,b^{3} c^{3} x^{3}}{3}-\frac {b^{4} c^{3} x^{4}}{4}+a^{4} c^{3} \ln \left (x \right )\) | \(44\) |
risch | \(-2 a^{3} b \,c^{3} x +\frac {2 a \,b^{3} c^{3} x^{3}}{3}-\frac {b^{4} c^{3} x^{4}}{4}+a^{4} c^{3} \ln \left (x \right )\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 43, normalized size = 0.91 \begin {gather*} -\frac {1}{4} \, b^{4} c^{3} x^{4} + \frac {2}{3} \, a b^{3} c^{3} x^{3} - 2 \, a^{3} b c^{3} x + a^{4} c^{3} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.67, size = 43, normalized size = 0.91 \begin {gather*} -\frac {1}{4} \, b^{4} c^{3} x^{4} + \frac {2}{3} \, a b^{3} c^{3} x^{3} - 2 \, a^{3} b c^{3} x + a^{4} c^{3} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 48, normalized size = 1.02 \begin {gather*} a^{4} c^{3} \log {\left (x \right )} - 2 a^{3} b c^{3} x + \frac {2 a b^{3} c^{3} x^{3}}{3} - \frac {b^{4} c^{3} x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.94, size = 44, normalized size = 0.94 \begin {gather*} -\frac {1}{4} \, b^{4} c^{3} x^{4} + \frac {2}{3} \, a b^{3} c^{3} x^{3} - 2 \, a^{3} b c^{3} x + a^{4} c^{3} \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 43, normalized size = 0.91 \begin {gather*} a^4\,c^3\,\ln \left (x\right )-\frac {b^4\,c^3\,x^4}{4}+\frac {2\,a\,b^3\,c^3\,x^3}{3}-2\,a^3\,b\,c^3\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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