Optimal. Leaf size=17 \[ \frac {c^2 (d+e x)^2}{2 e} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {27, 9} \[ \frac {c^2 (d+e x)^2}{2 e} \]
Antiderivative was successfully verified.
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Rule 9
Rule 27
Rubi steps
\begin {align*} \int \frac {\left (c d^2+2 c d e x+c e^2 x^2\right )^2}{(d+e x)^3} \, dx &=\int c^2 (d+e x) \, dx\\ &=\frac {c^2 (d+e x)^2}{2 e}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.94 \[ c^2 \left (d x+\frac {e x^2}{2}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.16, size = 16, normalized size = 0.94 \[ \frac {1}{2} \, c^{2} e x^{2} + c^{2} d x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 23, normalized size = 1.35 \[ \frac {1}{2} \, {\left (c^{2} x^{2} e^{7} + 2 \, c^{2} d x e^{6}\right )} e^{\left (-6\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 15, normalized size = 0.88 \[ \left (\frac {1}{2} e \,x^{2}+d x \right ) c^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 16, normalized size = 0.94 \[ \frac {1}{2} \, c^{2} e x^{2} + c^{2} d x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.76 \[ \frac {c^2\,x\,\left (2\,d+e\,x\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 15, normalized size = 0.88 \[ c^{2} d x + \frac {c^{2} e x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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