Optimal. Leaf size=18 \[ a^2 c x-\frac {1}{3} b^2 c x^3 \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {41} \[ a^2 c x-\frac {1}{3} b^2 c x^3 \]
Antiderivative was successfully verified.
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Rule 41
Rubi steps
\begin {align*} \int (a+b x) (a c-b c x) \, dx &=\int \left (a^2 c-b^2 c x^2\right ) \, dx\\ &=a^2 c x-\frac {1}{3} b^2 c x^3\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ c \left (a^2 x-\frac {b^2 x^3}{3}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 16, normalized size = 0.89 \[ -\frac {1}{3} x^{3} c b^{2} + x c a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.01, size = 16, normalized size = 0.89 \[ -\frac {1}{3} \, b^{2} c x^{3} + a^{2} c x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.94 \[ -\frac {1}{3} b^{2} c \,x^{3}+a^{2} c x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 16, normalized size = 0.89 \[ -\frac {1}{3} \, b^{2} c x^{3} + a^{2} c x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 18, normalized size = 1.00 \[ \frac {c\,x\,\left (3\,a^2-b^2\,x^2\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 15, normalized size = 0.83 \[ a^{2} c x - \frac {b^{2} c x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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