Optimal. Leaf size=97 \[ \frac{1}{5} x^5 (a f+b c)+\frac{1}{6} x^6 (a g+b d)+\frac{1}{7} x^7 (a h+b e)+\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{8} b f x^8+\frac{1}{9} b g x^9+\frac{1}{10} b h x^{10} \]
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Rubi [A] time = 0.0802172, antiderivative size = 97, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 34, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.029, Rules used = {1820} \[ \frac{1}{5} x^5 (a f+b c)+\frac{1}{6} x^6 (a g+b d)+\frac{1}{7} x^7 (a h+b e)+\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{8} b f x^8+\frac{1}{9} b g x^9+\frac{1}{10} b h x^{10} \]
Antiderivative was successfully verified.
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Rule 1820
Rubi steps
\begin{align*} \int x \left (a+b x^3\right ) \left (c+d x+e x^2+f x^3+g x^4+h x^5\right ) \, dx &=\int \left (a c x+a d x^2+a e x^3+(b c+a f) x^4+(b d+a g) x^5+(b e+a h) x^6+b f x^7+b g x^8+b h x^9\right ) \, dx\\ &=\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{5} (b c+a f) x^5+\frac{1}{6} (b d+a g) x^6+\frac{1}{7} (b e+a h) x^7+\frac{1}{8} b f x^8+\frac{1}{9} b g x^9+\frac{1}{10} b h x^{10}\\ \end{align*}
Mathematica [A] time = 0.0173656, size = 97, normalized size = 1. \[ \frac{1}{5} x^5 (a f+b c)+\frac{1}{6} x^6 (a g+b d)+\frac{1}{7} x^7 (a h+b e)+\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{8} b f x^8+\frac{1}{9} b g x^9+\frac{1}{10} b h x^{10} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 80, normalized size = 0.8 \begin{align*}{\frac{ac{x}^{2}}{2}}+{\frac{ad{x}^{3}}{3}}+{\frac{ae{x}^{4}}{4}}+{\frac{ \left ( af+bc \right ){x}^{5}}{5}}+{\frac{ \left ( ag+bd \right ){x}^{6}}{6}}+{\frac{ \left ( ah+be \right ){x}^{7}}{7}}+{\frac{bf{x}^{8}}{8}}+{\frac{bg{x}^{9}}{9}}+{\frac{bh{x}^{10}}{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.951365, size = 107, normalized size = 1.1 \begin{align*} \frac{1}{10} \, b h x^{10} + \frac{1}{9} \, b g x^{9} + \frac{1}{8} \, b f x^{8} + \frac{1}{7} \,{\left (b e + a h\right )} x^{7} + \frac{1}{6} \,{\left (b d + a g\right )} x^{6} + \frac{1}{4} \, a e x^{4} + \frac{1}{5} \,{\left (b c + a f\right )} x^{5} + \frac{1}{3} \, a d x^{3} + \frac{1}{2} \, a c x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.893111, size = 228, normalized size = 2.35 \begin{align*} \frac{1}{10} x^{10} h b + \frac{1}{9} x^{9} g b + \frac{1}{8} x^{8} f b + \frac{1}{7} x^{7} e b + \frac{1}{7} x^{7} h a + \frac{1}{6} x^{6} d b + \frac{1}{6} x^{6} g a + \frac{1}{5} x^{5} c b + \frac{1}{5} x^{5} f a + \frac{1}{4} x^{4} e a + \frac{1}{3} x^{3} d a + \frac{1}{2} x^{2} c a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.070509, size = 90, normalized size = 0.93 \begin{align*} \frac{a c x^{2}}{2} + \frac{a d x^{3}}{3} + \frac{a e x^{4}}{4} + \frac{b f x^{8}}{8} + \frac{b g x^{9}}{9} + \frac{b h x^{10}}{10} + x^{7} \left (\frac{a h}{7} + \frac{b e}{7}\right ) + x^{6} \left (\frac{a g}{6} + \frac{b d}{6}\right ) + x^{5} \left (\frac{a f}{5} + \frac{b c}{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05363, size = 117, normalized size = 1.21 \begin{align*} \frac{1}{10} \, b h x^{10} + \frac{1}{9} \, b g x^{9} + \frac{1}{8} \, b f x^{8} + \frac{1}{7} \, a h x^{7} + \frac{1}{7} \, b x^{7} e + \frac{1}{6} \, b d x^{6} + \frac{1}{6} \, a g x^{6} + \frac{1}{5} \, b c x^{5} + \frac{1}{5} \, a f x^{5} + \frac{1}{4} \, a x^{4} e + \frac{1}{3} \, a d x^{3} + \frac{1}{2} \, a c x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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