Optimal. Leaf size=16 \[ \frac {2 (c+d x)^{7/2}}{7 d} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {32} \[ \frac {2 (c+d x)^{7/2}}{7 d} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int (c+d x)^{5/2} \, dx &=\frac {2 (c+d x)^{7/2}}{7 d}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \[ \frac {2 (c+d x)^{7/2}}{7 d} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.42, size = 39, normalized size = 2.44 \[ \frac {2 \, {\left (d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right )} \sqrt {d x + c}}{7 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.78, size = 95, normalized size = 5.94 \[ \frac {2 \, {\left (5 \, {\left (d x + c\right )}^{\frac {7}{2}} - 21 \, {\left (d x + c\right )}^{\frac {5}{2}} c + 35 \, {\left (d x + c\right )}^{\frac {3}{2}} c^{2} + 35 \, {\left ({\left (d x + c\right )}^{\frac {3}{2}} - 3 \, \sqrt {d x + c} c\right )} c^{2} + 7 \, {\left (3 \, {\left (d x + c\right )}^{\frac {5}{2}} - 10 \, {\left (d x + c\right )}^{\frac {3}{2}} c + 15 \, \sqrt {d x + c} c^{2}\right )} c\right )}}{35 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ \frac {2 \left (d x +c \right )^{\frac {7}{2}}}{7 d} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 12, normalized size = 0.75 \[ \frac {2 \, {\left (d x + c\right )}^{\frac {7}{2}}}{7 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 12, normalized size = 0.75 \[ \frac {2\,{\left (c+d\,x\right )}^{7/2}}{7\,d} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 12, normalized size = 0.75 \[ \frac {2 \left (c + d x\right )^{\frac {7}{2}}}{7 d} \]
Verification of antiderivative is not currently implemented for this CAS.
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