Optimal. Leaf size=43 \[ \frac{3}{5} b^2 c x^5+\frac{b^3 x^3}{3}+\frac{3}{7} b c^2 x^7+\frac{c^3 x^9}{9} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0208536, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118, Rules used = {1584, 270} \[ \frac{3}{5} b^2 c x^5+\frac{b^3 x^3}{3}+\frac{3}{7} b c^2 x^7+\frac{c^3 x^9}{9} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1584
Rule 270
Rubi steps
\begin{align*} \int \frac{\left (b x^2+c x^4\right )^3}{x^4} \, dx &=\int x^2 \left (b+c x^2\right )^3 \, dx\\ &=\int \left (b^3 x^2+3 b^2 c x^4+3 b c^2 x^6+c^3 x^8\right ) \, dx\\ &=\frac{b^3 x^3}{3}+\frac{3}{5} b^2 c x^5+\frac{3}{7} b c^2 x^7+\frac{c^3 x^9}{9}\\ \end{align*}
Mathematica [A] time = 0.0019144, size = 43, normalized size = 1. \[ \frac{3}{5} b^2 c x^5+\frac{b^3 x^3}{3}+\frac{3}{7} b c^2 x^7+\frac{c^3 x^9}{9} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.043, size = 36, normalized size = 0.8 \begin{align*}{\frac{{b}^{3}{x}^{3}}{3}}+{\frac{3\,{b}^{2}c{x}^{5}}{5}}+{\frac{3\,b{c}^{2}{x}^{7}}{7}}+{\frac{{c}^{3}{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.05931, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{9} \, c^{3} x^{9} + \frac{3}{7} \, b c^{2} x^{7} + \frac{3}{5} \, b^{2} c x^{5} + \frac{1}{3} \, b^{3} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.199, size = 80, normalized size = 1.86 \begin{align*} \frac{1}{9} \, c^{3} x^{9} + \frac{3}{7} \, b c^{2} x^{7} + \frac{3}{5} \, b^{2} c x^{5} + \frac{1}{3} \, b^{3} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.074509, size = 39, normalized size = 0.91 \begin{align*} \frac{b^{3} x^{3}}{3} + \frac{3 b^{2} c x^{5}}{5} + \frac{3 b c^{2} x^{7}}{7} + \frac{c^{3} x^{9}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.29417, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{9} \, c^{3} x^{9} + \frac{3}{7} \, b c^{2} x^{7} + \frac{3}{5} \, b^{2} c x^{5} + \frac{1}{3} \, b^{3} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]