Optimal. Leaf size=19 \[ \frac {7}{8} \left (a+2 b x+c x^2\right )^{4/7} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {643}
\begin {gather*} \frac {7}{8} \left (a+2 b x+c x^2\right )^{4/7} \end {gather*}
Antiderivative was successfully verified.
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Rule 643
Rubi steps
\begin {align*} \int \frac {b+c x}{\left (a+2 b x+c x^2\right )^{3/7}} \, dx &=\frac {7}{8} \left (a+2 b x+c x^2\right )^{4/7}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 19, normalized size = 1.00 \begin {gather*} \frac {7}{8} (a+x (2 b+c x))^{4/7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.75, size = 16, normalized size = 0.84
method | result | size |
gosper | \(\frac {7 \left (c \,x^{2}+2 b x +a \right )^{\frac {4}{7}}}{8}\) | \(16\) |
default | \(\frac {7 \left (c \,x^{2}+2 b x +a \right )^{\frac {4}{7}}}{8}\) | \(16\) |
trager | \(\frac {7 \left (c \,x^{2}+2 b x +a \right )^{\frac {4}{7}}}{8}\) | \(16\) |
risch | \(\frac {7 \left (c \,x^{2}+2 b x +a \right )^{\frac {4}{7}}}{8}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 15, normalized size = 0.79 \begin {gather*} \frac {7}{8} \, {\left (c x^{2} + 2 \, b x + a\right )}^{\frac {4}{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.54, size = 15, normalized size = 0.79 \begin {gather*} \frac {7}{8} \, {\left (c x^{2} + 2 \, b x + a\right )}^{\frac {4}{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 17, normalized size = 0.89 \begin {gather*} \frac {7 \left (a + 2 b x + c x^{2}\right )^{\frac {4}{7}}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.94, size = 15, normalized size = 0.79 \begin {gather*} \frac {7}{8} \, {\left (c x^{2} + 2 \, b x + a\right )}^{\frac {4}{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.60, size = 15, normalized size = 0.79 \begin {gather*} \frac {7\,{\left (c\,x^2+2\,b\,x+a\right )}^{4/7}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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