Optimal. Leaf size=68 \[ -\frac {a A}{6 x^6}-\frac {a B}{5 x^5}-\frac {A b+a C}{4 x^4}-\frac {b B}{3 x^3}-\frac {A c+b C}{2 x^2}-\frac {B c}{x}+c C \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.03, antiderivative size = 68, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {1642}
\begin {gather*} -\frac {a C+A b}{4 x^4}-\frac {a A}{6 x^6}-\frac {a B}{5 x^5}-\frac {A c+b C}{2 x^2}-\frac {b B}{3 x^3}-\frac {B c}{x}+c C \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 1642
Rubi steps
\begin {align*} \int \frac {\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )}{x^7} \, dx &=\int \left (\frac {a A}{x^7}+\frac {a B}{x^6}+\frac {A b+a C}{x^5}+\frac {b B}{x^4}+\frac {A c+b C}{x^3}+\frac {B c}{x^2}+\frac {c C}{x}\right ) \, dx\\ &=-\frac {a A}{6 x^6}-\frac {a B}{5 x^5}-\frac {A b+a C}{4 x^4}-\frac {b B}{3 x^3}-\frac {A c+b C}{2 x^2}-\frac {B c}{x}+c C \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 68, normalized size = 1.00 \begin {gather*} -\frac {a (10 A+3 x (4 B+5 C x))+5 x^2 \left (3 A \left (b+2 c x^2\right )+2 x \left (2 b B+3 b C x+6 B c x^2\right )\right )}{60 x^6}+c C \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.01, size = 59, normalized size = 0.87
method | result | size |
default | \(-\frac {a B}{5 x^{5}}-\frac {A b +a C}{4 x^{4}}-\frac {A c +b C}{2 x^{2}}-\frac {B c}{x}-\frac {b B}{3 x^{3}}+c C \ln \left (x \right )-\frac {a A}{6 x^{6}}\) | \(59\) |
norman | \(\frac {\left (-\frac {A b}{4}-\frac {a C}{4}\right ) x^{2}+\left (-\frac {A c}{2}-\frac {b C}{2}\right ) x^{4}-\frac {a A}{6}-\frac {B b \,x^{3}}{3}-B c \,x^{5}-\frac {a B x}{5}}{x^{6}}+c C \ln \left (x \right )\) | \(61\) |
risch | \(\frac {\left (-\frac {A b}{4}-\frac {a C}{4}\right ) x^{2}+\left (-\frac {A c}{2}-\frac {b C}{2}\right ) x^{4}-\frac {a A}{6}-\frac {B b \,x^{3}}{3}-B c \,x^{5}-\frac {a B x}{5}}{x^{6}}+c C \ln \left (x \right )\) | \(61\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 59, normalized size = 0.87 \begin {gather*} C c \log \left (x\right ) - \frac {60 \, B c x^{5} + 20 \, B b x^{3} + 30 \, {\left (C b + A c\right )} x^{4} + 12 \, B a x + 15 \, {\left (C a + A b\right )} x^{2} + 10 \, A a}{60 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 62, normalized size = 0.91 \begin {gather*} \frac {60 \, C c x^{6} \log \left (x\right ) - 60 \, B c x^{5} - 20 \, B b x^{3} - 30 \, {\left (C b + A c\right )} x^{4} - 12 \, B a x - 15 \, {\left (C a + A b\right )} x^{2} - 10 \, A a}{60 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 9.68, size = 70, normalized size = 1.03 \begin {gather*} C c \log {\left (x \right )} + \frac {- 10 A a - 12 B a x - 20 B b x^{3} - 60 B c x^{5} + x^{4} \left (- 30 A c - 30 C b\right ) + x^{2} \left (- 15 A b - 15 C a\right )}{60 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 4.20, size = 60, normalized size = 0.88 \begin {gather*} C c \log \left ({\left | x \right |}\right ) - \frac {60 \, B c x^{5} + 20 \, B b x^{3} + 30 \, {\left (C b + A c\right )} x^{4} + 12 \, B a x + 15 \, {\left (C a + A b\right )} x^{2} + 10 \, A a}{60 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.79, size = 60, normalized size = 0.88 \begin {gather*} C\,c\,\ln \left (x\right )-\frac {B\,c\,x^5+\left (\frac {A\,c}{2}+\frac {C\,b}{2}\right )\,x^4+\frac {B\,b\,x^3}{3}+\left (\frac {A\,b}{4}+\frac {C\,a}{4}\right )\,x^2+\frac {B\,a\,x}{5}+\frac {A\,a}{6}}{x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________