Optimal. Leaf size=15 \[ \frac {1}{2 b (a-b x)^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {627, 32} \[ \frac {1}{2 b (a-b x)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 32
Rule 627
Rubi steps
\begin {align*} \int \frac {(a+b x)^3}{\left (a^2-b^2 x^2\right )^3} \, dx &=\int \frac {1}{(a-b x)^3} \, dx\\ &=\frac {1}{2 b (a-b x)^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \frac {1}{2 b (a-b x)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.87, size = 24, normalized size = 1.60 \[ \frac {1}{2 \, {\left (b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 14, normalized size = 0.93 \[ \frac {1}{2 \, {\left (b x - a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 15, normalized size = 1.00 \[ \frac {1}{2 \left (b x -a \right )^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.32, size = 24, normalized size = 1.60 \[ \frac {1}{2 \, {\left (b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.39, size = 24, normalized size = 1.60 \[ \frac {1}{2\,a^2\,b-4\,a\,b^2\,x+2\,b^3\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.23, size = 24, normalized size = 1.60 \[ \frac {1}{2 a^{2} b - 4 a b^{2} x + 2 b^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________