Optimal. Leaf size=34 \[ \frac {2}{3} \tanh ^{-1}\left (\frac {x^2+x-2}{\sqrt {x^4+2 x^3-3 x^2-5 x+2}}\right ) \]
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Rubi [F] time = 0.15, 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 {1+x}{\sqrt {2-5 x-3 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 {1+x}{\sqrt {2-5 x-3 x^2+2 x^3+x^4}} \, dx &=\int \left (\frac {1}{\sqrt {2-5 x-3 x^2+2 x^3+x^4}}+\frac {x}{\sqrt {2-5 x-3 x^2+2 x^3+x^4}}\right ) \, dx\\ &=\int \frac {1}{\sqrt {2-5 x-3 x^2+2 x^3+x^4}} \, dx+\int \frac {x}{\sqrt {2-5 x-3 x^2+2 x^3+x^4}} \, dx\\ \end {align*}
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Mathematica [C] time = 0.54, size = 830, normalized size = 24.41
result too large to display
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.16, size = 34, normalized size = 1.00 \begin {gather*} \frac {2}{3} \tanh ^{-1}\left (\frac {-2+x+x^2}{\sqrt {2-5 x-3 x^2+2 x^3+x^4}}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 38, normalized size = 1.12 \begin {gather*} \frac {1}{3} \, \log \left (2 \, x^{3} + 2 \, \sqrt {x^{4} + 2 \, x^{3} - 3 \, x^{2} - 5 \, x + 2} {\left (x - 1\right )} - 6 \, x + 3\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 {x + 1}{\sqrt {x^{4} + 2 \, x^{3} - 3 \, x^{2} - 5 \, x + 2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.12, size = 59, normalized size = 1.74
method | result | size |
trager | \(-\frac {\ln \left (-2 x^{3}+2 \sqrt {x^{4}+2 x^{3}-3 x^{2}-5 x +2}\, x -2 \sqrt {x^{4}+2 x^{3}-3 x^{2}-5 x +2}+6 x -3\right )}{3}\) | \(59\) |
default | \(\text {Expression too large to display}\) | \(2934\) |
elliptic | \(\text {Expression too large to display}\) | \(2934\) |
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 {x + 1}{\sqrt {x^{4} + 2 \, x^{3} - 3 \, x^{2} - 5 \, x + 2}}\,{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 = -0.03 \begin {gather*} \int \frac {x+1}{\sqrt {x^4+2\,x^3-3\,x^2-5\,x+2}} \,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 {x + 1}{\sqrt {\left (x + 2\right ) \left (x^{3} - 3 x + 1\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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