Optimal. Leaf size=36 \[ -\frac {(a+b x)^8}{9 a x^9}+\frac {b (a+b x)^8}{72 a^2 x^8} \]
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Rubi [A]
time = 0.00, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {47, 37}
\begin {gather*} \frac {b (a+b x)^8}{72 a^2 x^8}-\frac {(a+b x)^8}{9 a x^9} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 47
Rubi steps
\begin {align*} \int \frac {(a+b x)^7}{x^{10}} \, dx &=-\frac {(a+b x)^8}{9 a x^9}-\frac {b \int \frac {(a+b x)^7}{x^9} \, dx}{9 a}\\ &=-\frac {(a+b x)^8}{9 a x^9}+\frac {b (a+b x)^8}{72 a^2 x^8}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(91\) vs. \(2(36)=72\).
time = 0.00, size = 91, normalized size = 2.53 \begin {gather*} -\frac {a^7}{9 x^9}-\frac {7 a^6 b}{8 x^8}-\frac {3 a^5 b^2}{x^7}-\frac {35 a^4 b^3}{6 x^6}-\frac {7 a^3 b^4}{x^5}-\frac {21 a^2 b^5}{4 x^4}-\frac {7 a b^6}{3 x^3}-\frac {b^7}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(79\) vs.
\(2(32)=64\).
time = 0.07, size = 80, normalized size = 2.22
method | result | size |
norman | \(\frac {-\frac {1}{2} b^{7} x^{7}-\frac {7}{3} a \,b^{6} x^{6}-\frac {21}{4} a^{2} b^{5} x^{5}-7 a^{3} b^{4} x^{4}-\frac {35}{6} a^{4} b^{3} x^{3}-3 a^{5} b^{2} x^{2}-\frac {7}{8} a^{6} b x -\frac {1}{9} a^{7}}{x^{9}}\) | \(79\) |
risch | \(\frac {-\frac {1}{2} b^{7} x^{7}-\frac {7}{3} a \,b^{6} x^{6}-\frac {21}{4} a^{2} b^{5} x^{5}-7 a^{3} b^{4} x^{4}-\frac {35}{6} a^{4} b^{3} x^{3}-3 a^{5} b^{2} x^{2}-\frac {7}{8} a^{6} b x -\frac {1}{9} a^{7}}{x^{9}}\) | \(79\) |
gosper | \(-\frac {36 b^{7} x^{7}+168 a \,b^{6} x^{6}+378 a^{2} b^{5} x^{5}+504 a^{3} b^{4} x^{4}+420 a^{4} b^{3} x^{3}+216 a^{5} b^{2} x^{2}+63 a^{6} b x +8 a^{7}}{72 x^{9}}\) | \(80\) |
default | \(-\frac {7 a \,b^{6}}{3 x^{3}}-\frac {21 a^{2} b^{5}}{4 x^{4}}-\frac {a^{7}}{9 x^{9}}-\frac {b^{7}}{2 x^{2}}-\frac {7 a^{6} b}{8 x^{8}}-\frac {7 a^{3} b^{4}}{x^{5}}-\frac {35 a^{4} b^{3}}{6 x^{6}}-\frac {3 a^{5} b^{2}}{x^{7}}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 79 vs.
\(2 (32) = 64\).
time = 0.27, size = 79, normalized size = 2.19 \begin {gather*} -\frac {36 \, b^{7} x^{7} + 168 \, a b^{6} x^{6} + 378 \, a^{2} b^{5} x^{5} + 504 \, a^{3} b^{4} x^{4} + 420 \, a^{4} b^{3} x^{3} + 216 \, a^{5} b^{2} x^{2} + 63 \, a^{6} b x + 8 \, a^{7}}{72 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 79 vs.
\(2 (32) = 64\).
time = 0.44, size = 79, normalized size = 2.19 \begin {gather*} -\frac {36 \, b^{7} x^{7} + 168 \, a b^{6} x^{6} + 378 \, a^{2} b^{5} x^{5} + 504 \, a^{3} b^{4} x^{4} + 420 \, a^{4} b^{3} x^{3} + 216 \, a^{5} b^{2} x^{2} + 63 \, a^{6} b x + 8 \, a^{7}}{72 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 85 vs.
\(2 (29) = 58\).
time = 0.25, size = 85, normalized size = 2.36 \begin {gather*} \frac {- 8 a^{7} - 63 a^{6} b x - 216 a^{5} b^{2} x^{2} - 420 a^{4} b^{3} x^{3} - 504 a^{3} b^{4} x^{4} - 378 a^{2} b^{5} x^{5} - 168 a b^{6} x^{6} - 36 b^{7} x^{7}}{72 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 79 vs.
\(2 (32) = 64\).
time = 1.75, size = 79, normalized size = 2.19 \begin {gather*} -\frac {36 \, b^{7} x^{7} + 168 \, a b^{6} x^{6} + 378 \, a^{2} b^{5} x^{5} + 504 \, a^{3} b^{4} x^{4} + 420 \, a^{4} b^{3} x^{3} + 216 \, a^{5} b^{2} x^{2} + 63 \, a^{6} b x + 8 \, a^{7}}{72 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.00, size = 23, normalized size = 0.64 \begin {gather*} -\frac {\left (8\,a-b\,x\right )\,{\left (a+b\,x\right )}^8}{72\,a^2\,x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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