Optimal. Leaf size=2 \[ \tan (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {3852, 8}
\begin {gather*} \tan (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 3852
Rubi steps
\begin {align*} \int \sec ^2(x) \, dx &=-\text {Subst}(\int 1 \, dx,x,-\tan (x))\\ &=\tan (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 2, normalized size = 1.00 \begin {gather*} \tan (x) \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.65, size = 2, normalized size = 1.00 \begin {gather*} \text {Tan}\left [x\right ] \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 3, normalized size = 1.50
method | result | size |
default | \(\tan \left (x \right )\) | \(3\) |
risch | \(\frac {2 i}{{\mathrm e}^{2 i x}+1}\) | \(13\) |
norman | \(-\frac {2 \tan \left (\frac {x}{2}\right )}{\tan ^{2}\left (\frac {x}{2}\right )-1}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 2, normalized size = 1.00 \begin {gather*} \tan \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 7 vs.
\(2 (2) = 4\).
time = 0.34, size = 7, normalized size = 3.50 \begin {gather*} \frac {\sin \left (x\right )}{\cos \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 5 vs.
\(2 (2) = 4\)
time = 0.03, size = 5, normalized size = 2.50 \begin {gather*} \frac {\sin {\left (x \right )}}{\cos {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 6, normalized size = 3.00 \begin {gather*} \frac {2}{2} \tan x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 2, normalized size = 1.00 \begin {gather*} \mathrm {tan}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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