Optimal. Leaf size=88 \[ \frac{1}{3} x^3 (a f+b c)+\frac{1}{4} x^4 (a g+b d)+\frac{1}{5} x^5 (a h+b e)+a c \log (x)+a d x+\frac{1}{2} a e x^2+\frac{1}{6} b f x^6+\frac{1}{7} b g x^7+\frac{1}{8} b h x^8 \]
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Rubi [A] time = 0.122348, antiderivative size = 88, 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 \[ \frac{1}{3} x^3 (a f+b c)+\frac{1}{4} x^4 (a g+b d)+\frac{1}{5} x^5 (a h+b e)+a c \log (x)+a d x+\frac{1}{2} a e x^2+\frac{1}{6} b f x^6+\frac{1}{7} b g x^7+\frac{1}{8} b h x^8 \]
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,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a c \log{\left (x \right )} + a e \int x\, dx + \frac{b f x^{6}}{6} + \frac{b g x^{7}}{7} + \frac{b h x^{8}}{8} + d \int a\, dx + x^{5} \left (\frac{a h}{5} + \frac{b e}{5}\right ) + x^{4} \left (\frac{a g}{4} + \frac{b d}{4}\right ) + x^{3} \left (\frac{a f}{3} + \frac{b c}{3}\right ) \]
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,x)
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Mathematica [A] time = 0.0575435, size = 88, normalized size = 1. \[ \frac{1}{3} x^3 (a f+b c)+\frac{1}{4} x^4 (a g+b d)+\frac{1}{5} x^5 (a h+b e)+a c \log (x)+a d x+\frac{1}{2} a e x^2+\frac{1}{6} b f x^6+\frac{1}{7} b g x^7+\frac{1}{8} b h x^8 \]
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,x]
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Maple [A] time = 0.004, size = 81, normalized size = 0.9 \[{\frac{bh{x}^{8}}{8}}+{\frac{bg{x}^{7}}{7}}+{\frac{bf{x}^{6}}{6}}+{\frac{{x}^{5}ah}{5}}+{\frac{{x}^{5}be}{5}}+{\frac{{x}^{4}ag}{4}}+{\frac{bd{x}^{4}}{4}}+{\frac{{x}^{3}af}{3}}+{\frac{{x}^{3}bc}{3}}+{\frac{ae{x}^{2}}{2}}+adx+ac\ln \left ( x \right ) \]
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,x)
[Out]
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Maxima [A] time = 1.3777, size = 100, normalized size = 1.14 \[ \frac{1}{8} \, b h x^{8} + \frac{1}{7} \, b g x^{7} + \frac{1}{6} \, b f x^{6} + \frac{1}{5} \,{\left (b e + a h\right )} x^{5} + \frac{1}{4} \,{\left (b d + a g\right )} x^{4} + \frac{1}{2} \, a e x^{2} + \frac{1}{3} \,{\left (b c + a f\right )} x^{3} + a d x + a c \log \left (x\right ) \]
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,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244673, size = 100, normalized size = 1.14 \[ \frac{1}{8} \, b h x^{8} + \frac{1}{7} \, b g x^{7} + \frac{1}{6} \, b f x^{6} + \frac{1}{5} \,{\left (b e + a h\right )} x^{5} + \frac{1}{4} \,{\left (b d + a g\right )} x^{4} + \frac{1}{2} \, a e x^{2} + \frac{1}{3} \,{\left (b c + a f\right )} x^{3} + a d x + a c \log \left (x\right ) \]
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,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.69921, size = 85, normalized size = 0.97 \[ a c \log{\left (x \right )} + a d x + \frac{a e x^{2}}{2} + \frac{b f x^{6}}{6} + \frac{b g x^{7}}{7} + \frac{b h x^{8}}{8} + x^{5} \left (\frac{a h}{5} + \frac{b e}{5}\right ) + x^{4} \left (\frac{a g}{4} + \frac{b d}{4}\right ) + x^{3} \left (\frac{a f}{3} + \frac{b c}{3}\right ) \]
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,x)
[Out]
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GIAC/XCAS [A] time = 0.210309, size = 112, normalized size = 1.27 \[ \frac{1}{8} \, b h x^{8} + \frac{1}{7} \, b g x^{7} + \frac{1}{6} \, b f x^{6} + \frac{1}{5} \, a h x^{5} + \frac{1}{5} \, b x^{5} e + \frac{1}{4} \, b d x^{4} + \frac{1}{4} \, a g x^{4} + \frac{1}{3} \, b c x^{3} + \frac{1}{3} \, a f x^{3} + \frac{1}{2} \, a x^{2} e + a d x + a c{\rm ln}\left ({\left | x \right |}\right ) \]
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,x, algorithm="giac")
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