Integrand size = 30, antiderivative size = 88 \[ \int \left (a+b x^3\right )^2 \left (a c+a d x+b c x^3+b d x^4\right ) \, dx=a^3 c x+\frac {1}{2} a^3 d x^2+\frac {3}{4} a^2 b c x^4+\frac {3}{5} a^2 b d x^5+\frac {3}{7} a b^2 c x^7+\frac {3}{8} a b^2 d x^8+\frac {1}{10} b^3 c x^{10}+\frac {1}{11} b^3 d x^{11} \]
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Time = 0.04 (sec) , antiderivative size = 88, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {1864} \[ \int \left (a+b x^3\right )^2 \left (a c+a d x+b c x^3+b d x^4\right ) \, dx=a^3 c x+\frac {1}{2} a^3 d x^2+\frac {3}{4} a^2 b c x^4+\frac {3}{5} a^2 b d x^5+\frac {3}{7} a b^2 c x^7+\frac {3}{8} a b^2 d x^8+\frac {1}{10} b^3 c x^{10}+\frac {1}{11} b^3 d x^{11} \]
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Rule 1864
Rubi steps \begin{align*} \text {integral}& = \int \left (a^3 c+a^3 d x+3 a^2 b c x^3+3 a^2 b d x^4+3 a b^2 c x^6+3 a b^2 d x^7+b^3 c x^9+b^3 d x^{10}\right ) \, dx \\ & = a^3 c x+\frac {1}{2} a^3 d x^2+\frac {3}{4} a^2 b c x^4+\frac {3}{5} a^2 b d x^5+\frac {3}{7} a b^2 c x^7+\frac {3}{8} a b^2 d x^8+\frac {1}{10} b^3 c x^{10}+\frac {1}{11} b^3 d x^{11} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 88, normalized size of antiderivative = 1.00 \[ \int \left (a+b x^3\right )^2 \left (a c+a d x+b c x^3+b d x^4\right ) \, dx=a^3 c x+\frac {1}{2} a^3 d x^2+\frac {3}{4} a^2 b c x^4+\frac {3}{5} a^2 b d x^5+\frac {3}{7} a b^2 c x^7+\frac {3}{8} a b^2 d x^8+\frac {1}{10} b^3 c x^{10}+\frac {1}{11} b^3 d x^{11} \]
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Time = 1.48 (sec) , antiderivative size = 75, normalized size of antiderivative = 0.85
method | result | size |
default | \(a^{3} c x +\frac {1}{2} a^{3} d \,x^{2}+\frac {3}{4} a^{2} b c \,x^{4}+\frac {3}{5} x^{5} b d \,a^{2}+\frac {3}{7} a \,b^{2} c \,x^{7}+\frac {3}{8} x^{8} b^{2} d a +\frac {1}{10} b^{3} c \,x^{10}+\frac {1}{11} b^{3} d \,x^{11}\) | \(75\) |
norman | \(a^{3} c x +\frac {1}{2} a^{3} d \,x^{2}+\frac {3}{4} a^{2} b c \,x^{4}+\frac {3}{5} x^{5} b d \,a^{2}+\frac {3}{7} a \,b^{2} c \,x^{7}+\frac {3}{8} x^{8} b^{2} d a +\frac {1}{10} b^{3} c \,x^{10}+\frac {1}{11} b^{3} d \,x^{11}\) | \(75\) |
risch | \(a^{3} c x +\frac {1}{2} a^{3} d \,x^{2}+\frac {3}{4} a^{2} b c \,x^{4}+\frac {3}{5} x^{5} b d \,a^{2}+\frac {3}{7} a \,b^{2} c \,x^{7}+\frac {3}{8} x^{8} b^{2} d a +\frac {1}{10} b^{3} c \,x^{10}+\frac {1}{11} b^{3} d \,x^{11}\) | \(75\) |
parallelrisch | \(a^{3} c x +\frac {1}{2} a^{3} d \,x^{2}+\frac {3}{4} a^{2} b c \,x^{4}+\frac {3}{5} x^{5} b d \,a^{2}+\frac {3}{7} a \,b^{2} c \,x^{7}+\frac {3}{8} x^{8} b^{2} d a +\frac {1}{10} b^{3} c \,x^{10}+\frac {1}{11} b^{3} d \,x^{11}\) | \(75\) |
gosper | \(\frac {x \left (280 b^{3} d \,x^{10}+308 b^{3} c \,x^{9}+1155 a \,b^{2} d \,x^{7}+1320 a \,b^{2} c \,x^{6}+1848 a^{2} b d \,x^{4}+2310 a^{2} x^{3} b c +1540 a^{3} d x +3080 c \,a^{3}\right )}{3080}\) | \(76\) |
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Time = 0.38 (sec) , antiderivative size = 74, normalized size of antiderivative = 0.84 \[ \int \left (a+b x^3\right )^2 \left (a c+a d x+b c x^3+b d x^4\right ) \, dx=\frac {1}{11} \, b^{3} d x^{11} + \frac {1}{10} \, b^{3} c x^{10} + \frac {3}{8} \, a b^{2} d x^{8} + \frac {3}{7} \, a b^{2} c x^{7} + \frac {3}{5} \, a^{2} b d x^{5} + \frac {3}{4} \, a^{2} b c x^{4} + \frac {1}{2} \, a^{3} d x^{2} + a^{3} c x \]
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Time = 0.02 (sec) , antiderivative size = 90, normalized size of antiderivative = 1.02 \[ \int \left (a+b x^3\right )^2 \left (a c+a d x+b c x^3+b d x^4\right ) \, dx=a^{3} c x + \frac {a^{3} d x^{2}}{2} + \frac {3 a^{2} b c x^{4}}{4} + \frac {3 a^{2} b d x^{5}}{5} + \frac {3 a b^{2} c x^{7}}{7} + \frac {3 a b^{2} d x^{8}}{8} + \frac {b^{3} c x^{10}}{10} + \frac {b^{3} d x^{11}}{11} \]
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Time = 0.22 (sec) , antiderivative size = 74, normalized size of antiderivative = 0.84 \[ \int \left (a+b x^3\right )^2 \left (a c+a d x+b c x^3+b d x^4\right ) \, dx=\frac {1}{11} \, b^{3} d x^{11} + \frac {1}{10} \, b^{3} c x^{10} + \frac {3}{8} \, a b^{2} d x^{8} + \frac {3}{7} \, a b^{2} c x^{7} + \frac {3}{5} \, a^{2} b d x^{5} + \frac {3}{4} \, a^{2} b c x^{4} + \frac {1}{2} \, a^{3} d x^{2} + a^{3} c x \]
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Time = 0.27 (sec) , antiderivative size = 74, normalized size of antiderivative = 0.84 \[ \int \left (a+b x^3\right )^2 \left (a c+a d x+b c x^3+b d x^4\right ) \, dx=\frac {1}{11} \, b^{3} d x^{11} + \frac {1}{10} \, b^{3} c x^{10} + \frac {3}{8} \, a b^{2} d x^{8} + \frac {3}{7} \, a b^{2} c x^{7} + \frac {3}{5} \, a^{2} b d x^{5} + \frac {3}{4} \, a^{2} b c x^{4} + \frac {1}{2} \, a^{3} d x^{2} + a^{3} c x \]
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Time = 0.04 (sec) , antiderivative size = 74, normalized size of antiderivative = 0.84 \[ \int \left (a+b x^3\right )^2 \left (a c+a d x+b c x^3+b d x^4\right ) \, dx=\frac {d\,a^3\,x^2}{2}+c\,a^3\,x+\frac {3\,d\,a^2\,b\,x^5}{5}+\frac {3\,c\,a^2\,b\,x^4}{4}+\frac {3\,d\,a\,b^2\,x^8}{8}+\frac {3\,c\,a\,b^2\,x^7}{7}+\frac {d\,b^3\,x^{11}}{11}+\frac {c\,b^3\,x^{10}}{10} \]
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