Optimal. Leaf size=73 \[ \frac {4 (x-3) \sqrt {-x \left (\sqrt {x^2-x}-x\right )}}{15 x^2}-\frac {4 \sqrt {x^2-x} \sqrt {-x \left (\sqrt {x^2-x}-x\right )}}{15 x^2} \]
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Rubi [F] time = 0.17, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\sqrt {x^2-x \sqrt {-x+x^2}}}{x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\sqrt {x^2-x \sqrt {-x+x^2}}}{x^3} \, dx &=\int \frac {\sqrt {x^2-x \sqrt {-x+x^2}}}{x^3} \, dx\\ \end {align*}
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Mathematica [A] time = 0.21, size = 58, normalized size = 0.79 \begin {gather*} \frac {4 x \left (4 x^2-\left (4 \sqrt {(x-1) x}+9\right ) x+7 \sqrt {(x-1) x}+3\right )}{15 \left (x \left (x-\sqrt {(x-1) x}\right )\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 3.88, size = 73, normalized size = 1.00 \begin {gather*} \frac {4 (-3+x) \sqrt {-x \left (-x+\sqrt {-x+x^2}\right )}}{15 x^2}-\frac {4 \sqrt {-x+x^2} \sqrt {-x \left (-x+\sqrt {-x+x^2}\right )}}{15 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 37, normalized size = 0.51 \begin {gather*} \frac {4 \, \sqrt {x^{2} - \sqrt {x^{2} - x} x} {\left (x - \sqrt {x^{2} - x} - 3\right )}}{15 \, x^{2}} \end {gather*}
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 \begin {gather*} \int \frac {\sqrt {x^{2} - \sqrt {x^{2} - x} x}}{x^{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {\sqrt {x^{2}-x \sqrt {x^{2}-x}}}{x^{3}}\, dx\]
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 \begin {gather*} \int \frac {\sqrt {x^{2} - \sqrt {x^{2} - x} x}}{x^{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int \frac {\sqrt {x^2-x\,\sqrt {x^2-x}}}{x^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {x \left (x - \sqrt {x^{2} - x}\right )}}{x^{3}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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