Optimal. Leaf size=13 \[ \frac{\log (d+e x)}{c^3 e} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0046667, antiderivative size = 13, 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, 31} \[ \frac{\log (d+e x)}{c^3 e} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 12
Rule 31
Rubi steps
\begin{align*} \int \frac{(d+e x)^5}{\left (c d^2+2 c d e x+c e^2 x^2\right )^3} \, dx &=\int \frac{1}{c^3 (d+e x)} \, dx\\ &=\frac{\int \frac{1}{d+e x} \, dx}{c^3}\\ &=\frac{\log (d+e x)}{c^3 e}\\ \end{align*}
Mathematica [A] time = 0.0014406, size = 13, normalized size = 1. \[ \frac{\log (d+e x)}{c^3 e} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.039, size = 14, normalized size = 1.1 \begin{align*}{\frac{\ln \left ( ex+d \right ) }{{c}^{3}e}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.976387, size = 18, normalized size = 1.38 \begin{align*} \frac{\log \left (e x + d\right )}{c^{3} e} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.06933, size = 30, normalized size = 2.31 \begin{align*} \frac{\log \left (e x + d\right )}{c^{3} e} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.162682, size = 17, normalized size = 1.31 \begin{align*} \frac{\log{\left (c^{3} d + c^{3} e x \right )}}{c^{3} e} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: NotImplementedError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]