Optimal. Leaf size=16 \[ -\frac {1}{3 b \left (a+b x^3\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {267}
\begin {gather*} -\frac {1}{3 b \left (a+b x^3\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 267
Rubi steps
\begin {align*} \int \frac {x^2}{\left (a+b x^3\right )^2} \, dx &=-\frac {1}{3 b \left (a+b x^3\right )}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} -\frac {1}{3 b \left (a+b x^3\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.12, size = 15, normalized size = 0.94
method | result | size |
gosper | \(-\frac {1}{3 b \left (b \,x^{3}+a \right )}\) | \(15\) |
derivativedivides | \(-\frac {1}{3 b \left (b \,x^{3}+a \right )}\) | \(15\) |
default | \(-\frac {1}{3 b \left (b \,x^{3}+a \right )}\) | \(15\) |
norman | \(-\frac {1}{3 b \left (b \,x^{3}+a \right )}\) | \(15\) |
risch | \(-\frac {1}{3 b \left (b \,x^{3}+a \right )}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{3 \, {\left (b x^{3} + a\right )} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.34, size = 15, normalized size = 0.94 \begin {gather*} -\frac {1}{3 \, {\left (b^{2} x^{3} + a b\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.08, size = 15, normalized size = 0.94 \begin {gather*} - \frac {1}{3 a b + 3 b^{2} x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.15, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{3 \, {\left (b x^{3} + a\right )} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.97, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{3\,b\,\left (b\,x^3+a\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________