Integrand size = 29, antiderivative size = 14 \[ \int \left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^2 \, dx=\frac {(a+b x)^7}{7 b} \]
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Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {2084, 32} \[ \int \left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^2 \, dx=\frac {(a+b x)^7}{7 b} \]
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Rule 32
Rule 2084
Rubi steps \begin{align*} \text {integral}& = \int (a+b x)^6 \, dx \\ & = \frac {(a+b x)^7}{7 b} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^2 \, dx=\frac {(a+b x)^7}{7 b} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(64\) vs. \(2(12)=24\).
Time = 0.03 (sec) , antiderivative size = 65, normalized size of antiderivative = 4.64
method | result | size |
default | \(\frac {1}{7} b^{6} x^{7}+a \,b^{5} x^{6}+3 a^{2} b^{4} x^{5}+5 a^{3} b^{3} x^{4}+5 a^{4} b^{2} x^{3}+3 a^{5} b \,x^{2}+a^{6} x\) | \(65\) |
norman | \(\frac {1}{7} b^{6} x^{7}+a \,b^{5} x^{6}+3 a^{2} b^{4} x^{5}+5 a^{3} b^{3} x^{4}+5 a^{4} b^{2} x^{3}+3 a^{5} b \,x^{2}+a^{6} x\) | \(65\) |
risch | \(\frac {1}{7} b^{6} x^{7}+a \,b^{5} x^{6}+3 a^{2} b^{4} x^{5}+5 a^{3} b^{3} x^{4}+5 a^{4} b^{2} x^{3}+3 a^{5} b \,x^{2}+a^{6} x\) | \(65\) |
parallelrisch | \(\frac {1}{7} b^{6} x^{7}+a \,b^{5} x^{6}+3 a^{2} b^{4} x^{5}+5 a^{3} b^{3} x^{4}+5 a^{4} b^{2} x^{3}+3 a^{5} b \,x^{2}+a^{6} x\) | \(65\) |
gosper | \(\frac {x \left (b^{6} x^{6}+7 a \,b^{5} x^{5}+21 a^{2} b^{4} x^{4}+35 a^{3} b^{3} x^{3}+35 a^{4} b^{2} x^{2}+21 a^{5} b x +7 a^{6}\right )}{7}\) | \(66\) |
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Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (12) = 24\).
Time = 0.25 (sec) , antiderivative size = 64, normalized size of antiderivative = 4.57 \[ \int \left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^2 \, dx=\frac {1}{7} \, b^{6} x^{7} + a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{5} + 5 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{3} + 3 \, a^{5} b x^{2} + a^{6} x \]
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Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (8) = 16\).
Time = 0.03 (sec) , antiderivative size = 66, normalized size of antiderivative = 4.71 \[ \int \left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^2 \, dx=a^{6} x + 3 a^{5} b x^{2} + 5 a^{4} b^{2} x^{3} + 5 a^{3} b^{3} x^{4} + 3 a^{2} b^{4} x^{5} + a b^{5} x^{6} + \frac {b^{6} x^{7}}{7} \]
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Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (12) = 24\).
Time = 0.20 (sec) , antiderivative size = 99, normalized size of antiderivative = 7.07 \[ \int \left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^2 \, dx=\frac {1}{7} \, b^{6} x^{7} + a b^{5} x^{6} + \frac {9}{5} \, a^{2} b^{4} x^{5} + 3 \, a^{4} b^{2} x^{3} + a^{6} x + \frac {1}{2} \, {\left (b^{3} x^{4} + 4 \, a b^{2} x^{3} + 6 \, a^{2} b x^{2}\right )} a^{3} + \frac {3}{10} \, {\left (4 \, b^{3} x^{5} + 15 \, a b^{2} x^{4}\right )} a^{2} b \]
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Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (12) = 24\).
Time = 0.34 (sec) , antiderivative size = 64, normalized size of antiderivative = 4.57 \[ \int \left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^2 \, dx=\frac {1}{7} \, b^{6} x^{7} + a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{5} + 5 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{3} + 3 \, a^{5} b x^{2} + a^{6} x \]
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Time = 0.02 (sec) , antiderivative size = 64, normalized size of antiderivative = 4.57 \[ \int \left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^2 \, dx=a^6\,x+3\,a^5\,b\,x^2+5\,a^4\,b^2\,x^3+5\,a^3\,b^3\,x^4+3\,a^2\,b^4\,x^5+a\,b^5\,x^6+\frac {b^6\,x^7}{7} \]
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