Optimal. Leaf size=35 \[ \frac{3}{5} a^2 b x^5+\frac{a^3 x^7}{7}+a b^2 x^3+b^3 x \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0138719, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {263, 194} \[ \frac{3}{5} a^2 b x^5+\frac{a^3 x^7}{7}+a b^2 x^3+b^3 x \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 263
Rule 194
Rubi steps
\begin{align*} \int \left (a+\frac{b}{x^2}\right )^3 x^6 \, dx &=\int \left (b+a x^2\right )^3 \, dx\\ &=\int \left (b^3+3 a b^2 x^2+3 a^2 b x^4+a^3 x^6\right ) \, dx\\ &=b^3 x+a b^2 x^3+\frac{3}{5} a^2 b x^5+\frac{a^3 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0010596, size = 35, normalized size = 1. \[ \frac{3}{5} a^2 b x^5+\frac{a^3 x^7}{7}+a b^2 x^3+b^3 x \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 32, normalized size = 0.9 \begin{align*}{b}^{3}x+{x}^{3}a{b}^{2}+{\frac{3\,{a}^{2}b{x}^{5}}{5}}+{\frac{{a}^{3}{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.09346, size = 42, normalized size = 1.2 \begin{align*} \frac{1}{7} \, a^{3} x^{7} + \frac{3}{5} \, a^{2} b x^{5} + a b^{2} x^{3} + b^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.44121, size = 66, normalized size = 1.89 \begin{align*} \frac{1}{7} \, a^{3} x^{7} + \frac{3}{5} \, a^{2} b x^{5} + a b^{2} x^{3} + b^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.062721, size = 32, normalized size = 0.91 \begin{align*} \frac{a^{3} x^{7}}{7} + \frac{3 a^{2} b x^{5}}{5} + a b^{2} x^{3} + b^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.1397, size = 42, normalized size = 1.2 \begin{align*} \frac{1}{7} \, a^{3} x^{7} + \frac{3}{5} \, a^{2} b x^{5} + a b^{2} x^{3} + b^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]