Optimal. Leaf size=86 \[ -\frac{a f+b c}{x}+\log (x) (a g+b d)+x (a h+b e)-\frac{a c}{4 x^4}-\frac{a d}{3 x^3}-\frac{a e}{2 x^2}+\frac{1}{2} b f x^2+\frac{1}{3} b g x^3+\frac{1}{4} b h x^4 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.160798, antiderivative size = 86, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 36, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.028 \[ -\frac{a f+b c}{x}+\log (x) (a g+b d)+x (a h+b e)-\frac{a c}{4 x^4}-\frac{a d}{3 x^3}-\frac{a e}{2 x^2}+\frac{1}{2} b f x^2+\frac{1}{3} b g x^3+\frac{1}{4} b h x^4 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a c}{4 x^{4}} - \frac{a d}{3 x^{3}} - \frac{a e}{2 x^{2}} + b f \int x\, dx + \frac{b g x^{3}}{3} + \frac{b h x^{4}}{4} + \left (a g + b d\right ) \log{\left (x \right )} - \frac{a f + b c}{x} + \frac{\left (a h + b e\right ) \int a\, dx}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.118065, size = 77, normalized size = 0.9 \[ \log (x) (a g+b d)-\frac{a \left (3 c+4 d x+6 x^2 \left (e+2 f x-2 h x^3\right )\right )}{12 x^4}+b \left (-\frac{c}{x}+e x+\frac{1}{12} x^2 \left (6 f+4 g x+3 h x^2\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 76, normalized size = 0.9 \[{\frac{bh{x}^{4}}{4}}+{\frac{bg{x}^{3}}{3}}+{\frac{bf{x}^{2}}{2}}+xah+bex+\ln \left ( x \right ) ag+\ln \left ( x \right ) bd-{\frac{ac}{4\,{x}^{4}}}-{\frac{ad}{3\,{x}^{3}}}-{\frac{ae}{2\,{x}^{2}}}-{\frac{af}{x}}-{\frac{bc}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.38969, size = 101, normalized size = 1.17 \[ \frac{1}{4} \, b h x^{4} + \frac{1}{3} \, b g x^{3} + \frac{1}{2} \, b f x^{2} +{\left (b e + a h\right )} x +{\left (b d + a g\right )} \log \left (x\right ) - \frac{6 \, a e x^{2} + 12 \,{\left (b c + a f\right )} x^{3} + 4 \, a d x + 3 \, a c}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((h*x^5 + g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)/x^5,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.240342, size = 109, normalized size = 1.27 \[ \frac{3 \, b h x^{8} + 4 \, b g x^{7} + 6 \, b f x^{6} + 12 \,{\left (b e + a h\right )} x^{5} + 12 \,{\left (b d + a g\right )} x^{4} \log \left (x\right ) - 6 \, a e x^{2} - 12 \,{\left (b c + a f\right )} x^{3} - 4 \, a d x - 3 \, a c}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((h*x^5 + g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)/x^5,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 5.30844, size = 82, normalized size = 0.95 \[ \frac{b f x^{2}}{2} + \frac{b g x^{3}}{3} + \frac{b h x^{4}}{4} + x \left (a h + b e\right ) + \left (a g + b d\right ) \log{\left (x \right )} - \frac{3 a c + 4 a d x + 6 a e x^{2} + x^{3} \left (12 a f + 12 b c\right )}{12 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.212562, size = 104, normalized size = 1.21 \[ \frac{1}{4} \, b h x^{4} + \frac{1}{3} \, b g x^{3} + \frac{1}{2} \, b f x^{2} + a h x + b x e +{\left (b d + a g\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{12 \,{\left (b c + a f\right )} x^{3} + 6 \, a x^{2} e + 4 \, a d x + 3 \, a c}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((h*x^5 + g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)/x^5,x, algorithm="giac")
[Out]