Optimal. Leaf size=91 \[ \frac{2 a^2 \left (a+b x^3\right )^{11}}{11 b^5}-\frac{2 a^3 \left (a+b x^3\right )^{10}}{15 b^5}+\frac{a^4 \left (a+b x^3\right )^9}{27 b^5}+\frac{\left (a+b x^3\right )^{13}}{39 b^5}-\frac{a \left (a+b x^3\right )^{12}}{9 b^5} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.140358, antiderivative size = 91, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{2 a^2 \left (a+b x^3\right )^{11}}{11 b^5}-\frac{2 a^3 \left (a+b x^3\right )^{10}}{15 b^5}+\frac{a^4 \left (a+b x^3\right )^9}{27 b^5}+\frac{\left (a+b x^3\right )^{13}}{39 b^5}-\frac{a \left (a+b x^3\right )^{12}}{9 b^5} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^{14} \left (a+b x^3\right )^8 \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int x^4 (a+b x)^8 \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{a^4 (a+b x)^8}{b^4}-\frac{4 a^3 (a+b x)^9}{b^4}+\frac{6 a^2 (a+b x)^{10}}{b^4}-\frac{4 a (a+b x)^{11}}{b^4}+\frac{(a+b x)^{12}}{b^4}\right ) \, dx,x,x^3\right )\\ &=\frac{a^4 \left (a+b x^3\right )^9}{27 b^5}-\frac{2 a^3 \left (a+b x^3\right )^{10}}{15 b^5}+\frac{2 a^2 \left (a+b x^3\right )^{11}}{11 b^5}-\frac{a \left (a+b x^3\right )^{12}}{9 b^5}+\frac{\left (a+b x^3\right )^{13}}{39 b^5}\\ \end{align*}
Mathematica [A] time = 0.0029106, size = 108, normalized size = 1.19 \[ \frac{28}{33} a^2 b^6 x^{33}+\frac{28}{15} a^3 b^5 x^{30}+\frac{70}{27} a^4 b^4 x^{27}+\frac{7}{3} a^5 b^3 x^{24}+\frac{4}{3} a^6 b^2 x^{21}+\frac{4}{9} a^7 b x^{18}+\frac{a^8 x^{15}}{15}+\frac{2}{9} a b^7 x^{36}+\frac{b^8 x^{39}}{39} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 91, normalized size = 1. \begin{align*}{\frac{{b}^{8}{x}^{39}}{39}}+{\frac{2\,a{b}^{7}{x}^{36}}{9}}+{\frac{28\,{b}^{6}{a}^{2}{x}^{33}}{33}}+{\frac{28\,{a}^{3}{b}^{5}{x}^{30}}{15}}+{\frac{70\,{a}^{4}{b}^{4}{x}^{27}}{27}}+{\frac{7\,{a}^{5}{b}^{3}{x}^{24}}{3}}+{\frac{4\,{a}^{6}{b}^{2}{x}^{21}}{3}}+{\frac{4\,{a}^{7}b{x}^{18}}{9}}+{\frac{{a}^{8}{x}^{15}}{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.959494, size = 122, normalized size = 1.34 \begin{align*} \frac{1}{39} \, b^{8} x^{39} + \frac{2}{9} \, a b^{7} x^{36} + \frac{28}{33} \, a^{2} b^{6} x^{33} + \frac{28}{15} \, a^{3} b^{5} x^{30} + \frac{70}{27} \, a^{4} b^{4} x^{27} + \frac{7}{3} \, a^{5} b^{3} x^{24} + \frac{4}{3} \, a^{6} b^{2} x^{21} + \frac{4}{9} \, a^{7} b x^{18} + \frac{1}{15} \, a^{8} x^{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.39974, size = 224, normalized size = 2.46 \begin{align*} \frac{1}{39} x^{39} b^{8} + \frac{2}{9} x^{36} b^{7} a + \frac{28}{33} x^{33} b^{6} a^{2} + \frac{28}{15} x^{30} b^{5} a^{3} + \frac{70}{27} x^{27} b^{4} a^{4} + \frac{7}{3} x^{24} b^{3} a^{5} + \frac{4}{3} x^{21} b^{2} a^{6} + \frac{4}{9} x^{18} b a^{7} + \frac{1}{15} x^{15} a^{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.101437, size = 107, normalized size = 1.18 \begin{align*} \frac{a^{8} x^{15}}{15} + \frac{4 a^{7} b x^{18}}{9} + \frac{4 a^{6} b^{2} x^{21}}{3} + \frac{7 a^{5} b^{3} x^{24}}{3} + \frac{70 a^{4} b^{4} x^{27}}{27} + \frac{28 a^{3} b^{5} x^{30}}{15} + \frac{28 a^{2} b^{6} x^{33}}{33} + \frac{2 a b^{7} x^{36}}{9} + \frac{b^{8} x^{39}}{39} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.11355, size = 122, normalized size = 1.34 \begin{align*} \frac{1}{39} \, b^{8} x^{39} + \frac{2}{9} \, a b^{7} x^{36} + \frac{28}{33} \, a^{2} b^{6} x^{33} + \frac{28}{15} \, a^{3} b^{5} x^{30} + \frac{70}{27} \, a^{4} b^{4} x^{27} + \frac{7}{3} \, a^{5} b^{3} x^{24} + \frac{4}{3} \, a^{6} b^{2} x^{21} + \frac{4}{9} \, a^{7} b x^{18} + \frac{1}{15} \, a^{8} x^{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]