Optimal. Leaf size=21 \[ -\frac {a}{4 x^4}-\frac {b}{2 x^2}+c \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {14}
\begin {gather*} -\frac {a}{4 x^4}-\frac {b}{2 x^2}+c \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^2+c x^4}{x^5} \, dx &=\int \left (\frac {a}{x^5}+\frac {b}{x^3}+\frac {c}{x}\right ) \, dx\\ &=-\frac {a}{4 x^4}-\frac {b}{2 x^2}+c \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 21, normalized size = 1.00 \begin {gather*} -\frac {a}{4 x^4}-\frac {b}{2 x^2}+c \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 18, normalized size = 0.86
method | result | size |
default | \(-\frac {a}{4 x^{4}}-\frac {b}{2 x^{2}}+c \ln \left (x \right )\) | \(18\) |
norman | \(\frac {-\frac {b \,x^{2}}{2}-\frac {a}{4}}{x^{4}}+c \ln \left (x \right )\) | \(20\) |
risch | \(\frac {-\frac {b \,x^{2}}{2}-\frac {a}{4}}{x^{4}}+c \ln \left (x \right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 21, normalized size = 1.00 \begin {gather*} \frac {1}{2} \, c \log \left (x^{2}\right ) - \frac {2 \, b x^{2} + a}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 23, normalized size = 1.10 \begin {gather*} \frac {4 \, c x^{4} \log \left (x\right ) - 2 \, b x^{2} - a}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.09, size = 19, normalized size = 0.90 \begin {gather*} c \log {\left (x \right )} + \frac {- a - 2 b x^{2}}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 3.05, size = 27, normalized size = 1.29 \begin {gather*} \frac {1}{2} \, c \log \left (x^{2}\right ) - \frac {3 \, c x^{4} + 2 \, b x^{2} + a}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 20, normalized size = 0.95 \begin {gather*} c\,\ln \left (x\right )-\frac {\frac {b\,x^2}{2}+\frac {a}{4}}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________