Integrand size = 49, antiderivative size = 14 \[ \int \left (a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right ) \, dx=\frac {(a+b x)^6}{6 b} \]
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Leaf count is larger than twice the leaf count of optimal. \(61\) vs. \(2(14)=28\).
Time = 0.01 (sec) , antiderivative size = 61, normalized size of antiderivative = 4.36, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right ) \, dx=a^5 x+\frac {5}{2} a^4 b x^2+\frac {10}{3} a^3 b^2 x^3+\frac {5}{2} a^2 b^3 x^4+a b^4 x^5+\frac {b^5 x^6}{6} \]
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Rubi steps \begin{align*} \text {integral}& = a^5 x+\frac {5}{2} a^4 b x^2+\frac {10}{3} a^3 b^2 x^3+\frac {5}{2} a^2 b^3 x^4+a b^4 x^5+\frac {b^5 x^6}{6} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(61\) vs. \(2(14)=28\).
Time = 0.00 (sec) , antiderivative size = 61, normalized size of antiderivative = 4.36 \[ \int \left (a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right ) \, dx=a^5 x+\frac {5}{2} a^4 b x^2+\frac {10}{3} a^3 b^2 x^3+\frac {5}{2} a^2 b^3 x^4+a b^4 x^5+\frac {b^5 x^6}{6} \]
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Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93
method | result | size |
default | \(\frac {\left (b x +a \right )^{6}}{6 b}\) | \(13\) |
norman | \(\frac {1}{6} b^{5} x^{6}+a \,b^{4} x^{5}+\frac {5}{2} a^{2} b^{3} x^{4}+\frac {10}{3} a^{3} x^{3} b^{2}+\frac {5}{2} x^{2} a^{4} b +a^{5} x\) | \(54\) |
risch | \(\frac {1}{6} b^{5} x^{6}+a \,b^{4} x^{5}+\frac {5}{2} a^{2} b^{3} x^{4}+\frac {10}{3} a^{3} x^{3} b^{2}+\frac {5}{2} x^{2} a^{4} b +a^{5} x\) | \(54\) |
parallelrisch | \(\frac {1}{6} b^{5} x^{6}+a \,b^{4} x^{5}+\frac {5}{2} a^{2} b^{3} x^{4}+\frac {10}{3} a^{3} x^{3} b^{2}+\frac {5}{2} x^{2} a^{4} b +a^{5} x\) | \(54\) |
parts | \(\frac {1}{6} b^{5} x^{6}+a \,b^{4} x^{5}+\frac {5}{2} a^{2} b^{3} x^{4}+\frac {10}{3} a^{3} x^{3} b^{2}+\frac {5}{2} x^{2} a^{4} b +a^{5} x\) | \(54\) |
gosper | \(\frac {x \left (b^{5} x^{5}+6 a \,b^{4} x^{4}+15 a^{2} b^{3} x^{3}+20 a^{3} b^{2} x^{2}+15 x \,a^{4} b +6 a^{5}\right )}{6}\) | \(55\) |
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (12) = 24\).
Time = 0.28 (sec) , antiderivative size = 53, normalized size of antiderivative = 3.79 \[ \int \left (a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right ) \, dx=\frac {1}{6} \, b^{5} x^{6} + a b^{4} x^{5} + \frac {5}{2} \, a^{2} b^{3} x^{4} + \frac {10}{3} \, a^{3} b^{2} x^{3} + \frac {5}{2} \, a^{4} b x^{2} + a^{5} x \]
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Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (8) = 16\).
Time = 0.02 (sec) , antiderivative size = 60, normalized size of antiderivative = 4.29 \[ \int \left (a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right ) \, dx=a^{5} x + \frac {5 a^{4} b x^{2}}{2} + \frac {10 a^{3} b^{2} x^{3}}{3} + \frac {5 a^{2} b^{3} x^{4}}{2} + a b^{4} x^{5} + \frac {b^{5} x^{6}}{6} \]
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (12) = 24\).
Time = 0.20 (sec) , antiderivative size = 53, normalized size of antiderivative = 3.79 \[ \int \left (a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right ) \, dx=\frac {1}{6} \, b^{5} x^{6} + a b^{4} x^{5} + \frac {5}{2} \, a^{2} b^{3} x^{4} + \frac {10}{3} \, a^{3} b^{2} x^{3} + \frac {5}{2} \, a^{4} b x^{2} + a^{5} x \]
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (12) = 24\).
Time = 0.30 (sec) , antiderivative size = 53, normalized size of antiderivative = 3.79 \[ \int \left (a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right ) \, dx=\frac {1}{6} \, b^{5} x^{6} + a b^{4} x^{5} + \frac {5}{2} \, a^{2} b^{3} x^{4} + \frac {10}{3} \, a^{3} b^{2} x^{3} + \frac {5}{2} \, a^{4} b x^{2} + a^{5} x \]
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Time = 0.02 (sec) , antiderivative size = 53, normalized size of antiderivative = 3.79 \[ \int \left (a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right ) \, dx=a^5\,x+\frac {5\,a^4\,b\,x^2}{2}+\frac {10\,a^3\,b^2\,x^3}{3}+\frac {5\,a^2\,b^3\,x^4}{2}+a\,b^4\,x^5+\frac {b^5\,x^6}{6} \]
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