Optimal. Leaf size=21 \[ \frac{x^7}{7 a \left (a+b x^2\right )^{7/2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0045666, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {264} \[ \frac{x^7}{7 a \left (a+b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin{align*} \int \frac{x^6}{\left (a+b x^2\right )^{9/2}} \, dx &=\frac{x^7}{7 a \left (a+b x^2\right )^{7/2}}\\ \end{align*}
Mathematica [A] time = 0.0059893, size = 21, normalized size = 1. \[ \frac{x^7}{7 a \left (a+b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 18, normalized size = 0.9 \begin{align*}{\frac{{x}^{7}}{7\,a} \left ( b{x}^{2}+a \right ) ^{-{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 1.31785, size = 139, normalized size = 6.62 \begin{align*} -\frac{x^{5}}{2 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}} b} - \frac{5 \, a x^{3}}{8 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}} b^{2}} + \frac{x}{14 \,{\left (b x^{2} + a\right )}^{\frac{3}{2}} b^{3}} + \frac{x}{7 \, \sqrt{b x^{2} + a} a b^{3}} + \frac{3 \, a x}{56 \,{\left (b x^{2} + a\right )}^{\frac{5}{2}} b^{3}} - \frac{15 \, a^{2} x}{56 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}} b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.3269, size = 120, normalized size = 5.71 \begin{align*} \frac{\sqrt{b x^{2} + a} x^{7}}{7 \,{\left (a b^{4} x^{8} + 4 \, a^{2} b^{3} x^{6} + 6 \, a^{3} b^{2} x^{4} + 4 \, a^{4} b x^{2} + a^{5}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 2.00362, size = 95, normalized size = 4.52 \begin{align*} \frac{x^{7}}{7 a^{\frac{9}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 21 a^{\frac{7}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 21 a^{\frac{5}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 7 a^{\frac{3}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 3.00424, size = 23, normalized size = 1.1 \begin{align*} \frac{x^{7}}{7 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}} a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]