Optimal. Leaf size=3 \[ c x \]
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Rubi [A] time = 0.0037241, antiderivative size = 3, normalized size of antiderivative = 1., 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 = {24, 21, 8} \[ c x \]
Antiderivative was successfully verified.
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Rule 24
Rule 21
Rule 8
Rubi steps
\begin{align*} \int \frac{c d^2+2 c d e x+c e^2 x^2}{(d+e x)^2} \, dx &=\frac{\int \frac{c d e^2+c e^3 x}{d+e x} \, dx}{e^2}\\ &=c \int 1 \, dx\\ &=c x\\ \end{align*}
Mathematica [A] time = 0.0003464, size = 3, normalized size = 1. \[ c x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.038, size = 4, normalized size = 1.3 \begin{align*} cx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12504, size = 4, normalized size = 1.33 \begin{align*} c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.9908, size = 7, normalized size = 2.33 \begin{align*} c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.081061, size = 2, normalized size = 0.67 \begin{align*} c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [C] time = 1.16001, size = 149, normalized size = 49.67 \begin{align*} -2 \,{\left (e^{\left (-1\right )} \log \left (\frac{{\left | x e + d \right |} e^{\left (-1\right )}}{{\left (x e + d\right )}^{2}}\right ) - \frac{d e^{\left (-1\right )}}{x e + d}\right )} c d +{\left (2 \, d e^{\left (-3\right )} \log \left (\frac{{\left | x e + d \right |} e^{\left (-1\right )}}{{\left (x e + d\right )}^{2}}\right ) +{\left (x e + d\right )} e^{\left (-3\right )} - \frac{d^{2} e^{\left (-3\right )}}{x e + d}\right )} c e^{2} - \frac{c d^{2} e^{\left (-1\right )}}{x e + d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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