Optimal. Leaf size=17 \[ \frac{c^2 (d+e x)^7}{7 e} \]
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Rubi [A] time = 0.0048802, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {27, 12, 32} \[ \frac{c^2 (d+e x)^7}{7 e} \]
Antiderivative was successfully verified.
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Rule 27
Rule 12
Rule 32
Rubi steps
\begin{align*} \int (d+e x)^2 \left (c d^2+2 c d e x+c e^2 x^2\right )^2 \, dx &=\int c^2 (d+e x)^6 \, dx\\ &=c^2 \int (d+e x)^6 \, dx\\ &=\frac{c^2 (d+e x)^7}{7 e}\\ \end{align*}
Mathematica [A] time = 0.0026172, size = 17, normalized size = 1. \[ \frac{c^2 (d+e x)^7}{7 e} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.039, size = 86, normalized size = 5.1 \begin{align*}{\frac{{e}^{6}{c}^{2}{x}^{7}}{7}}+d{e}^{5}{c}^{2}{x}^{6}+3\,{d}^{2}{c}^{2}{e}^{4}{x}^{5}+5\,{d}^{3}{c}^{2}{e}^{3}{x}^{4}+5\,{d}^{4}{c}^{2}{e}^{2}{x}^{3}+3\,{d}^{5}{c}^{2}e{x}^{2}+{d}^{6}{c}^{2}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.14724, size = 115, normalized size = 6.76 \begin{align*} \frac{1}{7} \, c^{2} e^{6} x^{7} + c^{2} d e^{5} x^{6} + 3 \, c^{2} d^{2} e^{4} x^{5} + 5 \, c^{2} d^{3} e^{3} x^{4} + 5 \, c^{2} d^{4} e^{2} x^{3} + 3 \, c^{2} d^{5} e x^{2} + c^{2} d^{6} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.7823, size = 166, normalized size = 9.76 \begin{align*} \frac{1}{7} x^{7} e^{6} c^{2} + x^{6} e^{5} d c^{2} + 3 x^{5} e^{4} d^{2} c^{2} + 5 x^{4} e^{3} d^{3} c^{2} + 5 x^{3} e^{2} d^{4} c^{2} + 3 x^{2} e d^{5} c^{2} + x d^{6} c^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.089141, size = 90, normalized size = 5.29 \begin{align*} c^{2} d^{6} x + 3 c^{2} d^{5} e x^{2} + 5 c^{2} d^{4} e^{2} x^{3} + 5 c^{2} d^{3} e^{3} x^{4} + 3 c^{2} d^{2} e^{4} x^{5} + c^{2} d e^{5} x^{6} + \frac{c^{2} e^{6} x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.21732, size = 109, normalized size = 6.41 \begin{align*} \frac{1}{7} \, c^{2} x^{7} e^{6} + c^{2} d x^{6} e^{5} + 3 \, c^{2} d^{2} x^{5} e^{4} + 5 \, c^{2} d^{3} x^{4} e^{3} + 5 \, c^{2} d^{4} x^{3} e^{2} + 3 \, c^{2} d^{5} x^{2} e + c^{2} d^{6} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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