Optimal. Leaf size=20 \[ \frac {(x+1)^{7/2}}{7 (1-x)^{7/2}} \]
[Out]
________________________________________________________________________________________
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} \[ \frac {(x+1)^{7/2}}{7 (1-x)^{7/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rubi steps
\begin {align*} \int \frac {(1+x)^{5/2}}{(1-x)^{9/2}} \, dx &=\frac {(1+x)^{7/2}}{7 (1-x)^{7/2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \[ \frac {(x+1)^{7/2}}{7 (1-x)^{7/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.44, size = 66, normalized size = 3.30 \[ \frac {x^{4} - 4 \, x^{3} + 6 \, x^{2} + {\left (x^{3} + 3 \, x^{2} + 3 \, x + 1\right )} \sqrt {x + 1} \sqrt {-x + 1} - 4 \, x + 1}{7 \, {\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.11, size = 19, normalized size = 0.95 \[ \frac {{\left (x + 1\right )}^{\frac {7}{2}} \sqrt {-x + 1}}{7 \, {\left (x - 1\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 15, normalized size = 0.75 \[ \frac {\left (x +1\right )^{\frac {7}{2}}}{7 \left (-x +1\right )^{\frac {7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 1.36, size = 171, normalized size = 8.55 \[ \frac {{\left (-x^{2} + 1\right )}^{\frac {5}{2}}}{x^{6} - 6 \, x^{5} + 15 \, x^{4} - 20 \, x^{3} + 15 \, x^{2} - 6 \, x + 1} + \frac {5 \, {\left (-x^{2} + 1\right )}^{\frac {3}{2}}}{2 \, {\left (x^{5} - 5 \, x^{4} + 10 \, x^{3} - 10 \, x^{2} + 5 \, x - 1\right )}} + \frac {15 \, \sqrt {-x^{2} + 1}}{7 \, {\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} + \frac {3 \, \sqrt {-x^{2} + 1}}{14 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} - \frac {\sqrt {-x^{2} + 1}}{7 \, {\left (x^{2} - 2 \, x + 1\right )}} + \frac {\sqrt {-x^{2} + 1}}{7 \, {\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.28, size = 64, normalized size = 3.20 \[ \frac {\sqrt {1-x}\,\left (\frac {3\,x\,\sqrt {x+1}}{7}+\frac {\sqrt {x+1}}{7}+\frac {3\,x^2\,\sqrt {x+1}}{7}+\frac {x^3\,\sqrt {x+1}}{7}\right )}{x^4-4\,x^3+6\,x^2-4\,x+1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 19.49, size = 116, normalized size = 5.80 \[ \begin {cases} \frac {i \left (x + 1\right )^{\frac {7}{2}}}{7 \sqrt {x - 1} \left (x + 1\right )^{3} - 42 \sqrt {x - 1} \left (x + 1\right )^{2} + 84 \sqrt {x - 1} \left (x + 1\right ) - 56 \sqrt {x - 1}} & \text {for}\: \frac {\left |{x + 1}\right |}{2} > 1 \\- \frac {\left (x + 1\right )^{\frac {7}{2}}}{7 \sqrt {1 - x} \left (x + 1\right )^{3} - 42 \sqrt {1 - x} \left (x + 1\right )^{2} + 84 \sqrt {1 - x} \left (x + 1\right ) - 56 \sqrt {1 - x}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________