Optimal. Leaf size=71 \[ \frac {a^3 x^{m+1}}{m+1}+\frac {a^2 b x^{3 (m+1)}}{m+1}+\frac {3 a b^2 x^{5 (m+1)}}{5 (m+1)}+\frac {b^3 x^{7 (m+1)}}{7 (m+1)} \]
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Rubi [A] time = 0.04, antiderivative size = 71, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {270} \[ \frac {a^2 b x^{3 (m+1)}}{m+1}+\frac {a^3 x^{m+1}}{m+1}+\frac {3 a b^2 x^{5 (m+1)}}{5 (m+1)}+\frac {b^3 x^{7 (m+1)}}{7 (m+1)} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int x^m \left (a+b x^{2+2 m}\right )^3 \, dx &=\int \left (a^3 x^m+3 a^2 b x^{2+3 m}+3 a b^2 x^{4+5 m}+b^3 x^{6+7 m}\right ) \, dx\\ &=\frac {a^3 x^{1+m}}{1+m}+\frac {a^2 b x^{3 (1+m)}}{1+m}+\frac {3 a b^2 x^{5 (1+m)}}{5 (1+m)}+\frac {b^3 x^{7 (1+m)}}{7 (1+m)}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 57, normalized size = 0.80 \[ \frac {35 a^3 x^{m+1}+35 a^2 b x^{3 m+3}+21 a b^2 x^{5 m+5}+5 b^3 x^{7 m+7}}{35 m+35} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 58, normalized size = 0.82 \[ \frac {5 \, b^{3} x^{7} x^{7 \, m} + 21 \, a b^{2} x^{5} x^{5 \, m} + 35 \, a^{2} b x^{3} x^{3 \, m} + 35 \, a^{3} x x^{m}}{35 \, {\left (m + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 58, normalized size = 0.82 \[ \frac {5 \, b^{3} x^{7} x^{7 \, m} + 21 \, a b^{2} x^{5} x^{5 \, m} + 35 \, a^{2} b x^{3} x^{3 \, m} + 35 \, a^{3} x x^{m}}{35 \, {\left (m + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 70, normalized size = 0.99 \[ \frac {b^{3} x^{7} x^{7 m}}{7 m +7}+\frac {3 a \,b^{2} x^{5} x^{5 m}}{5 \left (m +1\right )}+\frac {a^{2} b \,x^{3} x^{3 m}}{m +1}+\frac {a^{3} x \,x^{m}}{m +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 67, normalized size = 0.94 \[ \frac {b^{3} x^{7 \, m + 7}}{7 \, {\left (m + 1\right )}} + \frac {3 \, a b^{2} x^{5 \, m + 5}}{5 \, {\left (m + 1\right )}} + \frac {a^{2} b x^{3 \, m + 3}}{m + 1} + \frac {a^{3} x^{m + 1}}{m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.45, size = 72, normalized size = 1.01 \[ \frac {a^3\,x\,x^m}{m+1}+\frac {b^3\,x^{7\,m}\,x^7}{7\,m+7}+\frac {a^2\,b\,x^{3\,m}\,x^3}{m+1}+\frac {3\,a\,b^2\,x^{5\,m}\,x^5}{5\,m+5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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