Optimal. Leaf size=17 \[ \frac {c^2 (d+e x)^5}{5 e} \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {27, 12, 32} \begin {gather*} \frac {c^2 (d+e x)^5}{5 e} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 32
Rubi steps
\begin {align*} \int \left (c d^2+2 c d e x+c e^2 x^2\right )^2 \, dx &=\int c^2 (d+e x)^4 \, dx\\ &=c^2 \int (d+e x)^4 \, dx\\ &=\frac {c^2 (d+e x)^5}{5 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)^5}{5 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 \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 = 0.36, size = 57, normalized size = 3.35 \begin {gather*} \frac {1}{5} x^{5} e^{4} c^{2} + x^{4} e^{3} d c^{2} + 2 x^{3} e^{2} d^{2} c^{2} + 2 x^{2} e d^{3} c^{2} + x d^{4} c^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 55, normalized size = 3.24 \begin {gather*} \frac {1}{5} \, c^{2} x^{5} e^{4} + c^{2} d x^{4} e^{3} + 2 \, c^{2} d^{2} x^{3} e^{2} + 2 \, c^{2} d^{3} x^{2} e + c^{2} d^{4} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 58, normalized size = 3.41 \begin {gather*} \frac {1}{5} c^{2} e^{4} x^{5}+c^{2} d \,e^{3} x^{4}+2 c^{2} d^{2} e^{2} x^{3}+2 c^{2} d^{3} e \,x^{2}+c^{2} d^{4} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.35, size = 68, normalized size = 4.00 \begin {gather*} \frac {1}{5} \, c^{2} e^{4} x^{5} + c^{2} d e^{3} x^{4} + \frac {4}{3} \, c^{2} d^{2} e^{2} x^{3} + c^{2} d^{4} x + \frac {2}{3} \, {\left (c e^{2} x^{3} + 3 \, c d e x^{2}\right )} c d^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 57, normalized size = 3.35 \begin {gather*} c^2\,d^4\,x+2\,c^2\,d^3\,e\,x^2+2\,c^2\,d^2\,e^2\,x^3+c^2\,d\,e^3\,x^4+\frac {c^2\,e^4\,x^5}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 60, normalized size = 3.53 \begin {gather*} c^{2} d^{4} x + 2 c^{2} d^{3} e x^{2} + 2 c^{2} d^{2} e^{2} x^{3} + c^{2} d e^{3} x^{4} + \frac {c^{2} e^{4} x^{5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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