Optimal. Leaf size=32 \[ 4 a c x+\frac {4 c^2 x^3}{3}+c d x^4+\frac {d^2 x^5}{5} \]
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Rubi [A] time = 0.01, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ 4 a c x+\frac {4 c^2 x^3}{3}+c d x^4+\frac {d^2 x^5}{5} \]
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right ) \, dx &=4 a c x+\frac {4 c^2 x^3}{3}+c d x^4+\frac {d^2 x^5}{5}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 32, normalized size = 1.00 \[ 4 a c x+\frac {4 c^2 x^3}{3}+c d x^4+\frac {d^2 x^5}{5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 28, normalized size = 0.88 \[ \frac {1}{5} x^{5} d^{2} + x^{4} d c + \frac {4}{3} x^{3} c^{2} + 4 x c a \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 28, normalized size = 0.88 \[ \frac {1}{5} \, d^{2} x^{5} + c d x^{4} + \frac {4}{3} \, c^{2} x^{3} + 4 \, a c x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 29, normalized size = 0.91 \[ \frac {1}{5} d^{2} x^{5}+c d \,x^{4}+\frac {4}{3} c^{2} x^{3}+4 a c x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 28, normalized size = 0.88 \[ \frac {1}{5} \, d^{2} x^{5} + c d x^{4} + \frac {4}{3} \, c^{2} x^{3} + 4 \, a c x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 28, normalized size = 0.88 \[ \frac {4\,c^2\,x^3}{3}+c\,d\,x^4+4\,a\,c\,x+\frac {d^2\,x^5}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 31, normalized size = 0.97 \[ 4 a c x + \frac {4 c^{2} x^{3}}{3} + c d x^{4} + \frac {d^{2} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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