Optimal. Leaf size=51 \[ \frac {8 \left (1-x^2\right )^{7/4}}{21 e (e x)^{7/2}}-\frac {2 \left (1-x^2\right )^{3/4}}{3 e (e x)^{7/2}} \]
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Rubi [A] time = 0.01, antiderivative size = 51, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {125, 273, 264} \[ \frac {8 \left (1-x^2\right )^{7/4}}{21 e (e x)^{7/2}}-\frac {2 \left (1-x^2\right )^{3/4}}{3 e (e x)^{7/2}} \]
Antiderivative was successfully verified.
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Rule 125
Rule 264
Rule 273
Rubi steps
\begin {align*} \int \frac {1}{\sqrt [4]{1-x} (e x)^{9/2} \sqrt [4]{1+x}} \, dx &=\int \frac {1}{(e x)^{9/2} \sqrt [4]{1-x^2}} \, dx\\ &=-\frac {2 \left (1-x^2\right )^{3/4}}{3 e (e x)^{7/2}}-\frac {4}{3} \int \frac {\left (1-x^2\right )^{3/4}}{(e x)^{9/2}} \, dx\\ &=-\frac {2 \left (1-x^2\right )^{3/4}}{3 e (e x)^{7/2}}+\frac {8 \left (1-x^2\right )^{7/4}}{21 e (e x)^{7/2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 35, normalized size = 0.69 \[ -\frac {2 \left (1-x^2\right )^{3/4} \left (4 x^2+3\right ) \sqrt {e x}}{21 e^5 x^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 32, normalized size = 0.63 \[ -\frac {2 \, \sqrt {e x} {\left (4 \, x^{2} + 3\right )} {\left (x + 1\right )}^{\frac {3}{4}} {\left (-x + 1\right )}^{\frac {3}{4}}}{21 \, e^{5} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (e x\right )^{\frac {9}{2}} {\left (x + 1\right )}^{\frac {1}{4}} {\left (-x + 1\right )}^{\frac {1}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 28, normalized size = 0.55 \[ -\frac {2 \left (x +1\right )^{\frac {3}{4}} \left (4 x^{2}+3\right ) \left (-x +1\right )^{\frac {3}{4}} x}{21 \left (e x \right )^{\frac {9}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (e x\right )^{\frac {9}{2}} {\left (x + 1\right )}^{\frac {1}{4}} {\left (-x + 1\right )}^{\frac {1}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.24, size = 44, normalized size = 0.86 \[ -\frac {\sqrt {e\,x}\,\left (\frac {2}{7\,e^5}+\frac {2\,x^2}{21\,e^5}-\frac {8\,x^4}{21\,e^5}\right )}{x^4\,{\left (1-x\right )}^{1/4}\,{\left (x+1\right )}^{1/4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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