Optimal. Leaf size=17 \[ \frac {c^2 (d+e x)^6}{6 e} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {27, 12, 32} \begin {gather*} \frac {c^2 (d+e x)^6}{6 e} \end {gather*}
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 )^2 \, dx &=\int c^2 (d+e x)^5 \, dx\\ &=c^2 \int (d+e x)^5 \, dx\\ &=\frac {c^2 (d+e x)^6}{6 e}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {c^2 (d+e x)^6}{6 e} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (d+e x) \left (c d^2+2 c d e x+c e^2 x^2\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.35, size = 71, normalized size = 4.18 \begin {gather*} \frac {1}{6} x^{6} e^{5} c^{2} + x^{5} e^{4} d c^{2} + \frac {5}{2} x^{4} e^{3} d^{2} c^{2} + \frac {10}{3} x^{3} e^{2} d^{3} c^{2} + \frac {5}{2} x^{2} e d^{4} c^{2} + x d^{5} c^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.22, size = 68, normalized size = 4.00 \begin {gather*} \frac {1}{6} \, c^{2} x^{6} e^{5} + c^{2} d x^{5} e^{4} + \frac {5}{2} \, c^{2} d^{2} x^{4} e^{3} + \frac {10}{3} \, c^{2} d^{3} x^{3} e^{2} + \frac {5}{2} \, c^{2} d^{4} x^{2} e + c^{2} d^{5} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 72, normalized size = 4.24 \begin {gather*} \frac {1}{6} c^{2} e^{5} x^{6}+c^{2} d \,e^{4} x^{5}+\frac {5}{2} c^{2} d^{2} e^{3} x^{4}+\frac {10}{3} c^{2} d^{3} e^{2} x^{3}+\frac {5}{2} c^{2} d^{4} e \,x^{2}+c^{2} d^{5} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 30, normalized size = 1.76 \begin {gather*} \frac {{\left (c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right )}^{3}}{6 \, c e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 71, normalized size = 4.18 \begin {gather*} c^2\,d^5\,x+\frac {5\,c^2\,d^4\,e\,x^2}{2}+\frac {10\,c^2\,d^3\,e^2\,x^3}{3}+\frac {5\,c^2\,d^2\,e^3\,x^4}{2}+c^2\,d\,e^4\,x^5+\frac {c^2\,e^5\,x^6}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.12, size = 80, normalized size = 4.71 \begin {gather*} c^{2} d^{5} x + \frac {5 c^{2} d^{4} e x^{2}}{2} + \frac {10 c^{2} d^{3} e^{2} x^{3}}{3} + \frac {5 c^{2} d^{2} e^{3} x^{4}}{2} + c^{2} d e^{4} x^{5} + \frac {c^{2} e^{5} x^{6}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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