Optimal. Leaf size=8 \[ -\arctan (1-x) \]
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Rubi [A]
time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {631, 210}
\begin {gather*} -\arctan (1-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 210
Rule 631
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\text {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-x\right )\\ &=-\arctan (1-x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} -\arctan (1-x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 5, normalized size = 0.62
method | result | size |
default | \(\arctan \left (x -1\right )\) | \(5\) |
risch | \(\arctan \left (x -1\right )\) | \(5\) |
parallelrisch | \(\frac {i \ln \left (x -1+i\right )}{2}-\frac {i \ln \left (x -1-i\right )}{2}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.47, size = 4, normalized size = 0.50 \begin {gather*} \arctan \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.56, size = 4, normalized size = 0.50 \begin {gather*} \arctan \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 3, normalized size = 0.38 \begin {gather*} \operatorname {atan}{\left (x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.52, size = 4, normalized size = 0.50 \begin {gather*} \arctan \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 4, normalized size = 0.50 \begin {gather*} \mathrm {atan}\left (x-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [A]
time = 1.00, size = 4, normalized size = 0.50 \begin {gather*} \arctan \left (x -1\right ) \end {gather*}
Antiderivative was successfully verified.
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