Optimal. Leaf size=51 \[ \frac{2 x^{15/2}}{35 a^2 \left (a x+b x^3\right )^{5/2}}+\frac{x^{17/2}}{7 a \left (a x+b x^3\right )^{7/2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0747788, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105, Rules used = {2015, 2014} \[ \frac{2 x^{15/2}}{35 a^2 \left (a x+b x^3\right )^{5/2}}+\frac{x^{17/2}}{7 a \left (a x+b x^3\right )^{7/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2015
Rule 2014
Rubi steps
\begin{align*} \int \frac{x^{17/2}}{\left (a x+b x^3\right )^{9/2}} \, dx &=\frac{x^{17/2}}{7 a \left (a x+b x^3\right )^{7/2}}+\frac{2 \int \frac{x^{15/2}}{\left (a x+b x^3\right )^{7/2}} \, dx}{7 a}\\ &=\frac{x^{17/2}}{7 a \left (a x+b x^3\right )^{7/2}}+\frac{2 x^{15/2}}{35 a^2 \left (a x+b x^3\right )^{5/2}}\\ \end{align*}
Mathematica [A] time = 0.0210368, size = 44, normalized size = 0.86 \[ \frac{x^{9/2} \sqrt{x \left (a+b x^2\right )} \left (7 a+2 b x^2\right )}{35 a^2 \left (a+b x^2\right )^4} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 37, normalized size = 0.7 \begin{align*}{\frac{ \left ( b{x}^{2}+a \right ) \left ( 2\,b{x}^{2}+7\,a \right ) }{35\,{a}^{2}}{x}^{{\frac{19}{2}}} \left ( b{x}^{3}+ax \right ) ^{-{\frac{9}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{\frac{17}{2}}}{{\left (b x^{3} + a x\right )}^{\frac{9}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.43253, size = 159, normalized size = 3.12 \begin{align*} \frac{{\left (2 \, b x^{6} + 7 \, a x^{4}\right )} \sqrt{b x^{3} + a x} \sqrt{x}}{35 \,{\left (a^{2} b^{4} x^{8} + 4 \, a^{3} b^{3} x^{6} + 6 \, a^{4} b^{2} x^{4} + 4 \, a^{5} b x^{2} + a^{6}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.33704, size = 39, normalized size = 0.76 \begin{align*} \frac{x^{5}{\left (\frac{2 \, b x^{2}}{a^{2}} + \frac{7}{a}\right )}}{35 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]