Optimal. Leaf size=15 \[ \frac {c (d+e x)^4}{4 e} \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {27, 12, 32} \[ \frac {c (d+e x)^4}{4 e} \]
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 32
Rubi steps
\begin {align*} \int (d+e x) \left (c d^2+2 c d e x+c e^2 x^2\right ) \, dx &=\int c (d+e x)^3 \, dx\\ &=c \int (d+e x)^3 \, dx\\ &=\frac {c (d+e x)^4}{4 e}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \frac {c (d+e x)^4}{4 e} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.79, size = 35, normalized size = 2.33 \[ \frac {1}{4} x^{4} e^{3} c + x^{3} e^{2} d c + \frac {3}{2} x^{2} e d^{2} c + x d^{3} c \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 34, normalized size = 2.27 \[ \frac {1}{4} \, c x^{4} e^{3} + c d x^{3} e^{2} + \frac {3}{2} \, c d^{2} x^{2} e + c d^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.19, size = 36, normalized size = 2.40 \[ \frac {1}{4} c \,e^{3} x^{4}+c d \,e^{2} x^{3}+\frac {3}{2} c \,d^{2} e \,x^{2}+c \,d^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.33, size = 30, normalized size = 2.00 \[ \frac {{\left (c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right )}^{2}}{4 \, c e} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 35, normalized size = 2.33 \[ c\,d^3\,x+\frac {3\,c\,d^2\,e\,x^2}{2}+c\,d\,e^2\,x^3+\frac {c\,e^3\,x^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 39, normalized size = 2.60 \[ c d^{3} x + \frac {3 c d^{2} e x^{2}}{2} + c d e^{2} x^{3} + \frac {c e^{3} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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