Optimal. Leaf size=18 \[ -\frac {2}{3} \left (\frac {1}{x^5}+\frac {1}{x^4}\right )^{3/2} x^6 \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {1979, 2000} \begin {gather*} -\frac {2}{3} \left (\frac {1}{x^4}+\frac {1}{x^5}\right )^{3/2} x^6 \end {gather*}
Antiderivative was successfully verified.
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Rule 1979
Rule 2000
Rubi steps
\begin {align*} \int \sqrt {\frac {1+x}{x^5}} \, dx &=\int \sqrt {\frac {1}{x^5}+\frac {1}{x^4}} \, dx\\ &=-\frac {2}{3} \left (\frac {1}{x^5}+\frac {1}{x^4}\right )^{3/2} x^6\\ \end {align*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.06 \begin {gather*} -\frac {2}{3} x (x+1) \sqrt {\frac {x+1}{x^5}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.03, size = 18, normalized size = 1.00 \begin {gather*} -\frac {2}{3} x^6 \left (\frac {x+1}{x^5}\right )^{3/2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 16, normalized size = 0.89 \begin {gather*} -\frac {2}{3} \, {\left (x^{2} + x\right )} \sqrt {\frac {x + 1}{x^{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.19, size = 50, normalized size = 2.78 \begin {gather*} \frac {2 \, {\left (3 \, {\left (x - \sqrt {x^{2} + x}\right )}^{2} \mathrm {sgn}\relax (x) + 3 \, {\left (x - \sqrt {x^{2} + x}\right )} \mathrm {sgn}\relax (x) + \mathrm {sgn}\relax (x)\right )}}{3 \, {\left (x - \sqrt {x^{2} + x}\right )}^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 16, normalized size = 0.89 \begin {gather*} -\frac {2 \left (x +1\right ) \sqrt {\frac {x +1}{x^{5}}}\, x}{3} \end {gather*}
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 \sqrt {\frac {x + 1}{x^{5}}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.26, size = 15, normalized size = 0.83 \begin {gather*} -\frac {2\,x\,\sqrt {\frac {x+1}{x^5}}\,\left (x+1\right )}{3} \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 \sqrt {\frac {x + 1}{x^{5}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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