Optimal. Leaf size=10 \[ -2 \cos \left (\pi \sqrt {x}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 3460, 2718}
\begin {gather*} -2 \cos \left (\pi \sqrt {x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2718
Rule 3460
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\pi \int \frac {\sin \left (\pi \sqrt {x}\right )}{\sqrt {x}} \, dx\\ &=(2 \pi ) \text {Subst}\left (\int \sin (\pi x) \, dx,x,\sqrt {x}\right )\\ &=-2 \cos \left (\pi \sqrt {x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 10, normalized size = 1.00 \begin {gather*} -2 \cos \left (\pi \sqrt {x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 9, normalized size = 0.90
method | result | size |
derivativedivides | \(-2 \cos \left (\pi \sqrt {x}\right )\) | \(9\) |
default | \(-2 \cos \left (\pi \sqrt {x}\right )\) | \(9\) |
meijerg | \(2 \sqrt {\pi }\, \left (\frac {1}{\sqrt {\pi }}-\frac {\cos \left (\pi \sqrt {x}\right )}{\sqrt {\pi }}\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 8, normalized size = 0.80 \begin {gather*} -2 \, \cos \left (\pi \sqrt {x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.60, size = 8, normalized size = 0.80 \begin {gather*} -2 \, \cos \left (\pi \sqrt {x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 10, normalized size = 1.00 \begin {gather*} - 2 \cos {\left (\pi \sqrt {x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.53, size = 8, normalized size = 0.80 \begin {gather*} -2 \, \cos \left (\pi \sqrt {x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.17, size = 8, normalized size = 0.80 \begin {gather*} -2\,\cos \left (\Pi \,\sqrt {x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 8, normalized size = 0.80 \begin {gather*} -\cos \left (\pi \sqrt {x}\right ) \end {gather*}
Warning: Unable to verify antiderivative.
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