Optimal. Leaf size=64 \[ -\log \left (-x^5-3 x^4-8 x^3-24 x^2+\left (x^3+2 x^2+4 x+8\right ) \sqrt {x^4+2 x^3+5 x^2+20 x-12}-16 x-16\right ) \]
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Rubi [F] time = 0.14, 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 {2+5 x}{\sqrt {-12+20 x+5 x^2+2 x^3+x^4}} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {2+5 x}{\sqrt {-12+20 x+5 x^2+2 x^3+x^4}} \, dx &=\int \left (\frac {2}{\sqrt {-12+20 x+5 x^2+2 x^3+x^4}}+\frac {5 x}{\sqrt {-12+20 x+5 x^2+2 x^3+x^4}}\right ) \, dx\\ &=2 \int \frac {1}{\sqrt {-12+20 x+5 x^2+2 x^3+x^4}} \, dx+5 \int \frac {x}{\sqrt {-12+20 x+5 x^2+2 x^3+x^4}} \, dx\\ \end {align*}
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Mathematica [C] time = 1.12, size = 1144, normalized size = 17.88
result too large to display
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 5.16, size = 64, normalized size = 1.00 \begin {gather*} -\log \left (-16-16 x-24 x^2-8 x^3-3 x^4-x^5+\left (8+4 x+2 x^2+x^3\right ) \sqrt {-12+20 x+5 x^2+2 x^3+x^4}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 58, normalized size = 0.91 \begin {gather*} \log \left (x^{5} + 3 \, x^{4} + 8 \, x^{3} + 24 \, x^{2} + \sqrt {x^{4} + 2 \, x^{3} + 5 \, x^{2} + 20 \, x - 12} {\left (x^{3} + 2 \, x^{2} + 4 \, x + 8\right )} + 16 \, x + 16\right ) \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 {5 \, x + 2}{\sqrt {x^{4} + 2 \, x^{3} + 5 \, x^{2} + 20 \, x - 12}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.24, size = 123, normalized size = 1.92
method | result | size |
trager | \(-\ln \left (-x^{5}+\sqrt {x^{4}+2 x^{3}+5 x^{2}+20 x -12}\, x^{3}-3 x^{4}+2 \sqrt {x^{4}+2 x^{3}+5 x^{2}+20 x -12}\, x^{2}-8 x^{3}+4 \sqrt {x^{4}+2 x^{3}+5 x^{2}+20 x -12}\, x -24 x^{2}+8 \sqrt {x^{4}+2 x^{3}+5 x^{2}+20 x -12}-16 x -16\right )\) | \(123\) |
default | \(\text {Expression too large to display}\) | \(2769\) |
elliptic | \(\text {Expression too large to display}\) | \(2769\) |
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 {5 \, x + 2}{\sqrt {x^{4} + 2 \, x^{3} + 5 \, x^{2} + 20 \, x - 12}}\,{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 = -0.02 \begin {gather*} \int \frac {5\,x+2}{\sqrt {x^4+2\,x^3+5\,x^2+20\,x-12}} \,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 {5 x + 2}{\sqrt {\left (x + 3\right ) \left (x^{3} - x^{2} + 8 x - 4\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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