Optimal. Leaf size=17 \[ \frac {c^2 (d+e x)^7}{7 e} \]
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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 = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {27, 12, 32} \[ \frac {c^2 (d+e x)^7}{7 e} \]
Antiderivative was successfully verified.
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Rule 12
Rule 27
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*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {c^2 (d+e x)^7}{7 e} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.68, size = 85, normalized size = 5.00 \[ \frac {1}{7} x^{7} e^{6} c^{2} + x^{6} e^{5} d c^{2} + 3 x^{5} e^{4} d^{2} c^{2} + 5 x^{4} e^{3} d^{3} c^{2} + 5 x^{3} e^{2} d^{4} c^{2} + 3 x^{2} e d^{5} c^{2} + x d^{6} c^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 81, normalized size = 4.76 \[ \frac {1}{7} \, c^{2} x^{7} e^{6} + c^{2} d x^{6} e^{5} + 3 \, c^{2} d^{2} x^{5} e^{4} + 5 \, c^{2} d^{3} x^{4} e^{3} + 5 \, c^{2} d^{4} x^{3} e^{2} + 3 \, c^{2} d^{5} x^{2} e + c^{2} d^{6} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 86, normalized size = 5.06 \[ \frac {1}{7} c^{2} e^{6} x^{7}+c^{2} d \,e^{5} x^{6}+3 c^{2} d^{2} e^{4} x^{5}+5 c^{2} d^{3} e^{3} x^{4}+5 c^{2} d^{4} e^{2} x^{3}+3 c^{2} d^{5} e \,x^{2}+c^{2} d^{6} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.30, size = 85, normalized size = 5.00 \[ \frac {1}{7} \, c^{2} e^{6} x^{7} + c^{2} d e^{5} x^{6} + 3 \, c^{2} d^{2} e^{4} x^{5} + 5 \, c^{2} d^{3} e^{3} x^{4} + 5 \, c^{2} d^{4} e^{2} x^{3} + 3 \, c^{2} d^{5} e x^{2} + c^{2} d^{6} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 85, normalized size = 5.00 \[ c^2\,d^6\,x+3\,c^2\,d^5\,e\,x^2+5\,c^2\,d^4\,e^2\,x^3+5\,c^2\,d^3\,e^3\,x^4+3\,c^2\,d^2\,e^4\,x^5+c^2\,d\,e^5\,x^6+\frac {c^2\,e^6\,x^7}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.10, size = 90, normalized size = 5.29 \[ c^{2} d^{6} x + 3 c^{2} d^{5} e x^{2} + 5 c^{2} d^{4} e^{2} x^{3} + 5 c^{2} d^{3} e^{3} x^{4} + 3 c^{2} d^{2} e^{4} x^{5} + c^{2} d e^{5} x^{6} + \frac {c^{2} e^{6} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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