Optimal. Leaf size=14 \[ -7+x+\frac {x}{1-25 i \pi } \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.29, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {8} \begin {gather*} \frac {(25 \pi +2 i) x}{25 \pi +i} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {(2 i+25 \pi ) x}{i+25 \pi }\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 28, normalized size = 2.00 \begin {gather*} -\frac {2 x}{-1+25 i \pi }+\frac {25 i \pi x}{-1+25 i \pi } \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.91, size = 14, normalized size = 1.00 \begin {gather*} \frac {{\left (25 \, \pi + 2 i\right )} x}{25 \, \pi + i} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 14, normalized size = 1.00 \begin {gather*} \frac {{\left (25 i \, \pi - 2\right )} x}{25 i \, \pi - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 1.21
method | result | size |
default | \(\frac {\left (25 i \pi -2\right ) x}{25 i \pi -1}\) | \(17\) |
norman | \(\frac {\left (625 \pi ^{2}+25 i \pi +2\right ) x}{625 \pi ^{2}+1}\) | \(23\) |
risch | \(\frac {25 i x \pi }{25 i \pi -1}-\frac {2 x}{25 i \pi -1}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 14, normalized size = 1.00 \begin {gather*} \frac {{\left (25 i \, \pi - 2\right )} x}{25 i \, \pi - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 16, normalized size = 1.14 \begin {gather*} \frac {x\,\left (-2+\Pi \,25{}\mathrm {i}\right )}{-1+\Pi \,25{}\mathrm {i}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.04, size = 14, normalized size = 1.00 \begin {gather*} \frac {x \left (-2 + 25 i \pi \right )}{-1 + 25 i \pi } \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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