Optimal. Leaf size=81 \[ \frac{6 a^2 (a+b x)^{13}}{13 b^5}-\frac{a^3 (a+b x)^{12}}{3 b^5}+\frac{a^4 (a+b x)^{11}}{11 b^5}+\frac{(a+b x)^{15}}{15 b^5}-\frac{2 a (a+b x)^{14}}{7 b^5} \]
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Rubi [A] time = 0.0390572, antiderivative size = 81, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ \frac{6 a^2 (a+b x)^{13}}{13 b^5}-\frac{a^3 (a+b x)^{12}}{3 b^5}+\frac{a^4 (a+b x)^{11}}{11 b^5}+\frac{(a+b x)^{15}}{15 b^5}-\frac{2 a (a+b x)^{14}}{7 b^5} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^4 (a+b x)^{10} \, dx &=\int \left (\frac{a^4 (a+b x)^{10}}{b^4}-\frac{4 a^3 (a+b x)^{11}}{b^4}+\frac{6 a^2 (a+b x)^{12}}{b^4}-\frac{4 a (a+b x)^{13}}{b^4}+\frac{(a+b x)^{14}}{b^4}\right ) \, dx\\ &=\frac{a^4 (a+b x)^{11}}{11 b^5}-\frac{a^3 (a+b x)^{12}}{3 b^5}+\frac{6 a^2 (a+b x)^{13}}{13 b^5}-\frac{2 a (a+b x)^{14}}{7 b^5}+\frac{(a+b x)^{15}}{15 b^5}\\ \end{align*}
Mathematica [A] time = 0.0033182, size = 130, normalized size = 1.6 \[ \frac{45}{13} a^2 b^8 x^{13}+10 a^3 b^7 x^{12}+\frac{210}{11} a^4 b^6 x^{11}+\frac{126}{5} a^5 b^5 x^{10}+\frac{70}{3} a^6 b^4 x^9+15 a^7 b^3 x^8+\frac{45}{7} a^8 b^2 x^7+\frac{5}{3} a^9 b x^6+\frac{a^{10} x^5}{5}+\frac{5}{7} a b^9 x^{14}+\frac{b^{10} x^{15}}{15} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 113, normalized size = 1.4 \begin{align*}{\frac{{b}^{10}{x}^{15}}{15}}+{\frac{5\,a{b}^{9}{x}^{14}}{7}}+{\frac{45\,{a}^{2}{b}^{8}{x}^{13}}{13}}+10\,{a}^{3}{b}^{7}{x}^{12}+{\frac{210\,{a}^{4}{b}^{6}{x}^{11}}{11}}+{\frac{126\,{a}^{5}{b}^{5}{x}^{10}}{5}}+{\frac{70\,{a}^{6}{b}^{4}{x}^{9}}{3}}+15\,{a}^{7}{b}^{3}{x}^{8}+{\frac{45\,{a}^{8}{b}^{2}{x}^{7}}{7}}+{\frac{5\,{a}^{9}b{x}^{6}}{3}}+{\frac{{a}^{10}{x}^{5}}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04508, size = 151, normalized size = 1.86 \begin{align*} \frac{1}{15} \, b^{10} x^{15} + \frac{5}{7} \, a b^{9} x^{14} + \frac{45}{13} \, a^{2} b^{8} x^{13} + 10 \, a^{3} b^{7} x^{12} + \frac{210}{11} \, a^{4} b^{6} x^{11} + \frac{126}{5} \, a^{5} b^{5} x^{10} + \frac{70}{3} \, a^{6} b^{4} x^{9} + 15 \, a^{7} b^{3} x^{8} + \frac{45}{7} \, a^{8} b^{2} x^{7} + \frac{5}{3} \, a^{9} b x^{6} + \frac{1}{5} \, a^{10} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.752, size = 271, normalized size = 3.35 \begin{align*} \frac{1}{15} x^{15} b^{10} + \frac{5}{7} x^{14} b^{9} a + \frac{45}{13} x^{13} b^{8} a^{2} + 10 x^{12} b^{7} a^{3} + \frac{210}{11} x^{11} b^{6} a^{4} + \frac{126}{5} x^{10} b^{5} a^{5} + \frac{70}{3} x^{9} b^{4} a^{6} + 15 x^{8} b^{3} a^{7} + \frac{45}{7} x^{7} b^{2} a^{8} + \frac{5}{3} x^{6} b a^{9} + \frac{1}{5} x^{5} a^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.104979, size = 131, normalized size = 1.62 \begin{align*} \frac{a^{10} x^{5}}{5} + \frac{5 a^{9} b x^{6}}{3} + \frac{45 a^{8} b^{2} x^{7}}{7} + 15 a^{7} b^{3} x^{8} + \frac{70 a^{6} b^{4} x^{9}}{3} + \frac{126 a^{5} b^{5} x^{10}}{5} + \frac{210 a^{4} b^{6} x^{11}}{11} + 10 a^{3} b^{7} x^{12} + \frac{45 a^{2} b^{8} x^{13}}{13} + \frac{5 a b^{9} x^{14}}{7} + \frac{b^{10} x^{15}}{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21715, size = 151, normalized size = 1.86 \begin{align*} \frac{1}{15} \, b^{10} x^{15} + \frac{5}{7} \, a b^{9} x^{14} + \frac{45}{13} \, a^{2} b^{8} x^{13} + 10 \, a^{3} b^{7} x^{12} + \frac{210}{11} \, a^{4} b^{6} x^{11} + \frac{126}{5} \, a^{5} b^{5} x^{10} + \frac{70}{3} \, a^{6} b^{4} x^{9} + 15 \, a^{7} b^{3} x^{8} + \frac{45}{7} \, a^{8} b^{2} x^{7} + \frac{5}{3} \, a^{9} b x^{6} + \frac{1}{5} \, a^{10} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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