Optimal. Leaf size=21 \[ -\frac {\left (a+b x^3\right )^{2/3}}{2 a x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {264} \[ -\frac {\left (a+b x^3\right )^{2/3}}{2 a x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin {align*} \int \frac {1}{x^3 \sqrt [3]{a+b x^3}} \, dx &=-\frac {\left (a+b x^3\right )^{2/3}}{2 a x^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 21, normalized size = 1.00 \[ -\frac {\left (a+b x^3\right )^{2/3}}{2 a x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.66, size = 17, normalized size = 0.81 \[ -\frac {{\left (b x^{3} + a\right )}^{\frac {2}{3}}}{2 \, a x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b x^{3} + a\right )}^{\frac {1}{3}} x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 18, normalized size = 0.86 \[ -\frac {\left (b \,x^{3}+a \right )^{\frac {2}{3}}}{2 a \,x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.34, size = 17, normalized size = 0.81 \[ -\frac {{\left (b x^{3} + a\right )}^{\frac {2}{3}}}{2 \, a x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.03, size = 17, normalized size = 0.81 \[ -\frac {{\left (b\,x^3+a\right )}^{2/3}}{2\,a\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 1.29, size = 31, normalized size = 1.48 \[ \frac {b^{\frac {2}{3}} \left (\frac {a}{b x^{3}} + 1\right )^{\frac {2}{3}} \Gamma \left (- \frac {2}{3}\right )}{3 a \Gamma \left (\frac {1}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________