Optimal. Leaf size=28 \[ -\frac {a^2}{4 x^4}-\frac {2 a b}{x}+\frac {b^2 x^2}{2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {276}
\begin {gather*} -\frac {a^2}{4 x^4}-\frac {2 a b}{x}+\frac {b^2 x^2}{2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 276
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^2}{x^5} \, dx &=\int \left (\frac {a^2}{x^5}+\frac {2 a b}{x^2}+b^2 x\right ) \, dx\\ &=-\frac {a^2}{4 x^4}-\frac {2 a b}{x}+\frac {b^2 x^2}{2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 28, normalized size = 1.00 \begin {gather*} -\frac {a^2}{4 x^4}-\frac {2 a b}{x}+\frac {b^2 x^2}{2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.12, size = 25, normalized size = 0.89
method | result | size |
gosper | \(-\frac {-2 b^{2} x^{6}+8 a b \,x^{3}+a^{2}}{4 x^{4}}\) | \(25\) |
default | \(-\frac {a^{2}}{4 x^{4}}-\frac {2 a b}{x}+\frac {b^{2} x^{2}}{2}\) | \(25\) |
norman | \(\frac {\frac {1}{2} b^{2} x^{6}-2 a b \,x^{3}-\frac {1}{4} a^{2}}{x^{4}}\) | \(26\) |
risch | \(\frac {b^{2} x^{2}}{2}+\frac {-2 a b \,x^{3}-\frac {1}{4} a^{2}}{x^{4}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 25, normalized size = 0.89 \begin {gather*} \frac {1}{2} \, b^{2} x^{2} - \frac {8 \, a b x^{3} + a^{2}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.34, size = 26, normalized size = 0.93 \begin {gather*} \frac {2 \, b^{2} x^{6} - 8 \, a b x^{3} - a^{2}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 26, normalized size = 0.93 \begin {gather*} \frac {b^{2} x^{2}}{2} + \frac {- a^{2} - 8 a b x^{3}}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.38, size = 25, normalized size = 0.89 \begin {gather*} \frac {1}{2} \, b^{2} x^{2} - \frac {8 \, a b x^{3} + a^{2}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 27, normalized size = 0.96 \begin {gather*} \frac {b^2\,x^2}{2}-\frac {\frac {a^2}{4}+2\,b\,a\,x^3}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________