Optimal. Leaf size=62 \[ -\frac {a^5}{7 x^7}-\frac {5 a^4 b}{4 x^4}-\frac {10 a^3 b^2}{x}+5 a^2 b^3 x^2+a b^4 x^5+\frac {b^5 x^8}{8} \]
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Rubi [A]
time = 0.02, antiderivative size = 62, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {276}
\begin {gather*} -\frac {a^5}{7 x^7}-\frac {5 a^4 b}{4 x^4}-\frac {10 a^3 b^2}{x}+5 a^2 b^3 x^2+a b^4 x^5+\frac {b^5 x^8}{8} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5}{x^8} \, dx &=\int \left (\frac {a^5}{x^8}+\frac {5 a^4 b}{x^5}+\frac {10 a^3 b^2}{x^2}+10 a^2 b^3 x+5 a b^4 x^4+b^5 x^7\right ) \, dx\\ &=-\frac {a^5}{7 x^7}-\frac {5 a^4 b}{4 x^4}-\frac {10 a^3 b^2}{x}+5 a^2 b^3 x^2+a b^4 x^5+\frac {b^5 x^8}{8}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 62, normalized size = 1.00 \begin {gather*} -\frac {a^5}{7 x^7}-\frac {5 a^4 b}{4 x^4}-\frac {10 a^3 b^2}{x}+5 a^2 b^3 x^2+a b^4 x^5+\frac {b^5 x^8}{8} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 57, normalized size = 0.92
method | result | size |
default | \(-\frac {a^{5}}{7 x^{7}}-\frac {5 a^{4} b}{4 x^{4}}-\frac {10 a^{3} b^{2}}{x}+5 a^{2} x^{2} b^{3}+a \,b^{4} x^{5}+\frac {b^{5} x^{8}}{8}\) | \(57\) |
norman | \(\frac {-\frac {1}{7} a^{5}-\frac {5}{4} a^{4} b \,x^{3}-10 a^{3} b^{2} x^{6}+5 a^{2} b^{3} x^{9}+a \,b^{4} x^{12}+\frac {1}{8} b^{5} x^{15}}{x^{7}}\) | \(58\) |
risch | \(\frac {b^{5} x^{8}}{8}+a \,b^{4} x^{5}+5 a^{2} x^{2} b^{3}+\frac {-10 a^{3} b^{2} x^{6}-\frac {5}{4} a^{4} b \,x^{3}-\frac {1}{7} a^{5}}{x^{7}}\) | \(59\) |
gosper | \(-\frac {-7 b^{5} x^{15}-56 a \,b^{4} x^{12}-280 a^{2} b^{3} x^{9}+560 a^{3} b^{2} x^{6}+70 a^{4} b \,x^{3}+8 a^{5}}{56 x^{7}}\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 59, normalized size = 0.95 \begin {gather*} \frac {1}{8} \, b^{5} x^{8} + a b^{4} x^{5} + 5 \, a^{2} b^{3} x^{2} - \frac {280 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 4 \, a^{5}}{28 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 59, normalized size = 0.95 \begin {gather*} \frac {7 \, b^{5} x^{15} + 56 \, a b^{4} x^{12} + 280 \, a^{2} b^{3} x^{9} - 560 \, a^{3} b^{2} x^{6} - 70 \, a^{4} b x^{3} - 8 \, a^{5}}{56 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 61, normalized size = 0.98 \begin {gather*} 5 a^{2} b^{3} x^{2} + a b^{4} x^{5} + \frac {b^{5} x^{8}}{8} + \frac {- 4 a^{5} - 35 a^{4} b x^{3} - 280 a^{3} b^{2} x^{6}}{28 x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.77, size = 59, normalized size = 0.95 \begin {gather*} \frac {1}{8} \, b^{5} x^{8} + a b^{4} x^{5} + 5 \, a^{2} b^{3} x^{2} - \frac {280 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 4 \, a^{5}}{28 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 59, normalized size = 0.95 \begin {gather*} \frac {b^5\,x^8}{8}-\frac {\frac {a^5}{7}+\frac {5\,a^4\,b\,x^3}{4}+10\,a^3\,b^2\,x^6}{x^7}+a\,b^4\,x^5+5\,a^2\,b^3\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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