Optimal. Leaf size=14 \[ -\frac {1}{7 d (c+d x)^7} \]
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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 {1}{7 d (c+d x)^7} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int \frac {1}{(c+d x)^8} \, dx &=-\frac {1}{7 d (c+d x)^7}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} -\frac {1}{7 d (c+d x)^7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 13, normalized size = 0.93
method | result | size |
gosper | \(-\frac {1}{7 d \left (d x +c \right )^{7}}\) | \(13\) |
default | \(-\frac {1}{7 d \left (d x +c \right )^{7}}\) | \(13\) |
norman | \(-\frac {1}{7 d \left (d x +c \right )^{7}}\) | \(13\) |
risch | \(-\frac {1}{7 d \left (d x +c \right )^{7}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 12, normalized size = 0.86 \begin {gather*} -\frac {1}{7 \, {\left (d x + c\right )}^{7} d} \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.
\(2 (12) = 24\).
time = 0.45, size = 79, normalized size = 5.64 \begin {gather*} -\frac {1}{7 \, {\left (d^{8} x^{7} + 7 \, c d^{7} x^{6} + 21 \, c^{2} d^{6} x^{5} + 35 \, c^{3} d^{5} x^{4} + 35 \, c^{4} d^{4} x^{3} + 21 \, c^{5} d^{3} x^{2} + 7 \, c^{6} d^{2} x + c^{7} d\right )}} \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.
\(2 (12) = 24\).
time = 0.22, size = 85, normalized size = 6.07 \begin {gather*} - \frac {1}{7 c^{7} d + 49 c^{6} d^{2} x + 147 c^{5} d^{3} x^{2} + 245 c^{4} d^{4} x^{3} + 245 c^{3} d^{5} x^{4} + 147 c^{2} d^{6} x^{5} + 49 c d^{7} x^{6} + 7 d^{8} x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.00, size = 12, normalized size = 0.86 \begin {gather*} -\frac {1}{7 \, {\left (d x + c\right )}^{7} d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.22, size = 81, normalized size = 5.79 \begin {gather*} -\frac {1}{7\,c^7\,d+49\,c^6\,d^2\,x+147\,c^5\,d^3\,x^2+245\,c^4\,d^4\,x^3+245\,c^3\,d^5\,x^4+147\,c^2\,d^6\,x^5+49\,c\,d^7\,x^6+7\,d^8\,x^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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