Optimal. Leaf size=14 \[ -\frac{3}{5} x \left (\frac{b}{x^4}\right )^{2/3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0015081, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {15, 30} \[ -\frac{3}{5} x \left (\frac{b}{x^4}\right )^{2/3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \left (\frac{b}{x^4}\right )^{2/3} \, dx &=\left (\left (\frac{b}{x^4}\right )^{2/3} x^{8/3}\right ) \int \frac{1}{x^{8/3}} \, dx\\ &=-\frac{3}{5} \left (\frac{b}{x^4}\right )^{2/3} x\\ \end{align*}
Mathematica [A] time = 0.0013227, size = 14, normalized size = 1. \[ -\frac{3}{5} x \left (\frac{b}{x^4}\right )^{2/3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 11, normalized size = 0.8 \begin{align*} -{\frac{3\,x}{5} \left ({\frac{b}{{x}^{4}}} \right ) ^{{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.973675, size = 14, normalized size = 1. \begin{align*} -\frac{3}{5} \, x \left (\frac{b}{x^{4}}\right )^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.71728, size = 30, normalized size = 2.14 \begin{align*} -\frac{3}{5} \, x \left (\frac{b}{x^{4}}\right )^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.443952, size = 19, normalized size = 1.36 \begin{align*} - \frac{3 b^{\frac{2}{3}} x \left (\frac{1}{x^{4}}\right )^{\frac{2}{3}}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (\frac{b}{x^{4}}\right )^{\frac{2}{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]