Optimal. Leaf size=14 \[ \frac {(a+b x)^8}{8 b} \]
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Rubi [A]
time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32}
\begin {gather*} \frac {(a+b x)^8}{8 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int (a+b x)^7 \, dx &=\frac {(a+b x)^8}{8 b}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {(a+b x)^8}{8 b} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 13, normalized size = 0.93
method | result | size |
default | \(\frac {\left (b x +a \right )^{8}}{8 b}\) | \(13\) |
gosper | \(\frac {1}{8} b^{7} x^{8}+a \,b^{6} x^{7}+\frac {7}{2} a^{2} b^{5} x^{6}+7 a^{3} b^{4} x^{5}+\frac {35}{4} a^{4} b^{3} x^{4}+7 a^{5} b^{2} x^{3}+\frac {7}{2} a^{6} b \,x^{2}+a^{7} x\) | \(76\) |
norman | \(\frac {1}{8} b^{7} x^{8}+a \,b^{6} x^{7}+\frac {7}{2} a^{2} b^{5} x^{6}+7 a^{3} b^{4} x^{5}+\frac {35}{4} a^{4} b^{3} x^{4}+7 a^{5} b^{2} x^{3}+\frac {7}{2} a^{6} b \,x^{2}+a^{7} x\) | \(76\) |
risch | \(\frac {b^{7} x^{8}}{8}+a \,b^{6} x^{7}+\frac {7 a^{2} b^{5} x^{6}}{2}+7 a^{3} b^{4} x^{5}+\frac {35 a^{4} b^{3} x^{4}}{4}+7 a^{5} b^{2} x^{3}+\frac {7 a^{6} b \,x^{2}}{2}+a^{7} x +\frac {a^{8}}{8 b}\) | \(84\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 12, normalized size = 0.86 \begin {gather*} \frac {{\left (b x + a\right )}^{8}}{8 \, b} \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. 75 vs.
\(2 (12) = 24\).
time = 1.16, size = 75, normalized size = 5.36 \begin {gather*} \frac {1}{8} \, b^{7} x^{8} + a b^{6} x^{7} + \frac {7}{2} \, a^{2} b^{5} x^{6} + 7 \, a^{3} b^{4} x^{5} + \frac {35}{4} \, a^{4} b^{3} x^{4} + 7 \, a^{5} b^{2} x^{3} + \frac {7}{2} \, a^{6} b x^{2} + a^{7} x \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. 83 vs.
\(2 (8) = 16\).
time = 0.01, size = 83, normalized size = 5.93 \begin {gather*} a^{7} x + \frac {7 a^{6} b x^{2}}{2} + 7 a^{5} b^{2} x^{3} + \frac {35 a^{4} b^{3} x^{4}}{4} + 7 a^{3} b^{4} x^{5} + \frac {7 a^{2} b^{5} x^{6}}{2} + a b^{6} x^{7} + \frac {b^{7} x^{8}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.29, size = 12, normalized size = 0.86 \begin {gather*} \frac {{\left (b x + a\right )}^{8}}{8 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 75, normalized size = 5.36 \begin {gather*} a^7\,x+\frac {7\,a^6\,b\,x^2}{2}+7\,a^5\,b^2\,x^3+\frac {35\,a^4\,b^3\,x^4}{4}+7\,a^3\,b^4\,x^5+\frac {7\,a^2\,b^5\,x^6}{2}+a\,b^6\,x^7+\frac {b^7\,x^8}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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