Optimal. Leaf size=17 \[ -\frac {a}{6 x^6}-\frac {b}{2 x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14}
\begin {gather*} -\frac {a}{6 x^6}-\frac {b}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^4}{x^7} \, dx &=\int \left (\frac {a}{x^7}+\frac {b}{x^3}\right ) \, dx\\ &=-\frac {a}{6 x^6}-\frac {b}{2 x^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {a}{6 x^6}-\frac {b}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 14, normalized size = 0.82
method | result | size |
gosper | \(-\frac {3 b \,x^{4}+a}{6 x^{6}}\) | \(14\) |
default | \(-\frac {a}{6 x^{6}}-\frac {b}{2 x^{2}}\) | \(14\) |
norman | \(\frac {-\frac {b \,x^{4}}{2}-\frac {a}{6}}{x^{6}}\) | \(15\) |
risch | \(\frac {-\frac {b \,x^{4}}{2}-\frac {a}{6}}{x^{6}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 13, normalized size = 0.76 \begin {gather*} -\frac {3 \, b x^{4} + a}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 13, normalized size = 0.76 \begin {gather*} -\frac {3 \, b x^{4} + a}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 14, normalized size = 0.82 \begin {gather*} \frac {- a - 3 b x^{4}}{6 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 2.05, size = 13, normalized size = 0.76 \begin {gather*} -\frac {3 \, b x^{4} + a}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 13, normalized size = 0.76 \begin {gather*} -\frac {3\,b\,x^4+a}{6\,x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________