Optimal. Leaf size=17 \[ \frac{x^3}{3 a (a+b x)^3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0016848, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {37} \[ \frac{x^3}{3 a (a+b x)^3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rubi steps
\begin{align*} \int \frac{x^2}{(a+b x)^4} \, dx &=\frac{x^3}{3 a (a+b x)^3}\\ \end{align*}
Mathematica [A] time = 0.0171861, size = 31, normalized size = 1.82 \[ -\frac{a^2+3 a b x+3 b^2 x^2}{3 b^3 (a+b x)^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0.004, size = 41, normalized size = 2.4 \begin{align*} -{\frac{1}{{b}^{3} \left ( bx+a \right ) }}+{\frac{a}{{b}^{3} \left ( bx+a \right ) ^{2}}}-{\frac{{a}^{2}}{3\,{b}^{3} \left ( bx+a \right ) ^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 1.08234, size = 73, normalized size = 4.29 \begin{align*} -\frac{3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \,{\left (b^{6} x^{3} + 3 \, a b^{5} x^{2} + 3 \, a^{2} b^{4} x + a^{3} b^{3}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.48234, size = 111, normalized size = 6.53 \begin{align*} -\frac{3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \,{\left (b^{6} x^{3} + 3 \, a b^{5} x^{2} + 3 \, a^{2} b^{4} x + a^{3} b^{3}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.516355, size = 56, normalized size = 3.29 \begin{align*} - \frac{a^{2} + 3 a b x + 3 b^{2} x^{2}}{3 a^{3} b^{3} + 9 a^{2} b^{4} x + 9 a b^{5} x^{2} + 3 b^{6} x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13832, size = 39, normalized size = 2.29 \begin{align*} -\frac{3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \,{\left (b x + a\right )}^{3} b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]