Optimal. Leaf size=20 \[ \frac {(x+1)^{5/2}}{5 (1-x)^{5/2}} \]
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Rubi [A] time = 0.00, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {37} \[ \frac {(x+1)^{5/2}}{5 (1-x)^{5/2}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {(1+x)^{3/2}}{(1-x)^{7/2}} \, dx &=\frac {(1+x)^{5/2}}{5 (1-x)^{5/2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \[ \frac {(x+1)^{5/2}}{5 (1-x)^{5/2}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.44, size = 52, normalized size = 2.60 \[ \frac {x^{3} - 3 \, x^{2} - {\left (x^{2} + 2 \, x + 1\right )} \sqrt {x + 1} \sqrt {-x + 1} + 3 \, x - 1}{5 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.06, size = 19, normalized size = 0.95 \[ -\frac {{\left (x + 1\right )}^{\frac {5}{2}} \sqrt {-x + 1}}{5 \, {\left (x - 1\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.75 \[ \frac {\left (x +1\right )^{\frac {5}{2}}}{5 \left (-x +1\right )^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.28, size = 94, normalized size = 4.70 \[ \frac {{\left (-x^{2} + 1\right )}^{\frac {3}{2}}}{x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1} + \frac {6 \, \sqrt {-x^{2} + 1}}{5 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} + \frac {\sqrt {-x^{2} + 1}}{5 \, {\left (x^{2} - 2 \, x + 1\right )}} - \frac {\sqrt {-x^{2} + 1}}{5 \, {\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 50, normalized size = 2.50 \[ -\frac {\sqrt {1-x}\,\left (\frac {2\,x\,\sqrt {x+1}}{5}+\frac {\sqrt {x+1}}{5}+\frac {x^2\,\sqrt {x+1}}{5}\right )}{x^3-3\,x^2+3\,x-1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 6.26, size = 88, normalized size = 4.40 \[ \begin {cases} - \frac {i \left (x + 1\right )^{\frac {5}{2}}}{5 \sqrt {x - 1} \left (x + 1\right )^{2} - 20 \sqrt {x - 1} \left (x + 1\right ) + 20 \sqrt {x - 1}} & \text {for}\: \frac {\left |{x + 1}\right |}{2} > 1 \\\frac {\left (x + 1\right )^{\frac {5}{2}}}{5 \sqrt {1 - x} \left (x + 1\right )^{2} - 20 \sqrt {1 - x} \left (x + 1\right ) + 20 \sqrt {1 - x}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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