Optimal. Leaf size=36 \[ \frac{2}{17} b^2 x^{17/2}+\frac{4}{21} b c x^{21/2}+\frac{2}{25} c^2 x^{25/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0160419, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105, Rules used = {1584, 270} \[ \frac{2}{17} b^2 x^{17/2}+\frac{4}{21} b c x^{21/2}+\frac{2}{25} c^2 x^{25/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1584
Rule 270
Rubi steps
\begin{align*} \int x^{7/2} \left (b x^2+c x^4\right )^2 \, dx &=\int x^{15/2} \left (b+c x^2\right )^2 \, dx\\ &=\int \left (b^2 x^{15/2}+2 b c x^{19/2}+c^2 x^{23/2}\right ) \, dx\\ &=\frac{2}{17} b^2 x^{17/2}+\frac{4}{21} b c x^{21/2}+\frac{2}{25} c^2 x^{25/2}\\ \end{align*}
Mathematica [A] time = 0.008169, size = 30, normalized size = 0.83 \[ \frac{2 x^{17/2} \left (525 b^2+850 b c x^2+357 c^2 x^4\right )}{8925} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.045, size = 27, normalized size = 0.8 \begin{align*}{\frac{714\,{c}^{2}{x}^{4}+1700\,bc{x}^{2}+1050\,{b}^{2}}{8925}{x}^{{\frac{17}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.963226, size = 32, normalized size = 0.89 \begin{align*} \frac{2}{25} \, c^{2} x^{\frac{25}{2}} + \frac{4}{21} \, b c x^{\frac{21}{2}} + \frac{2}{17} \, b^{2} x^{\frac{17}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.2389, size = 81, normalized size = 2.25 \begin{align*} \frac{2}{8925} \,{\left (357 \, c^{2} x^{12} + 850 \, b c x^{10} + 525 \, b^{2} x^{8}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 41.1167, size = 34, normalized size = 0.94 \begin{align*} \frac{2 b^{2} x^{\frac{17}{2}}}{17} + \frac{4 b c x^{\frac{21}{2}}}{21} + \frac{2 c^{2} x^{\frac{25}{2}}}{25} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.15506, size = 32, normalized size = 0.89 \begin{align*} \frac{2}{25} \, c^{2} x^{\frac{25}{2}} + \frac{4}{21} \, b c x^{\frac{21}{2}} + \frac{2}{17} \, b^{2} x^{\frac{17}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]