Optimal. Leaf size=10 \[ \frac {\text {Chi}(b x)^2}{2} \]
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Rubi [A]
time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {6818}
\begin {gather*} \frac {\text {Chi}(b x)^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rubi steps
\begin {align*} \int \frac {\cosh (b x) \text {Chi}(b x)}{x} \, dx &=\frac {\text {Chi}(b x)^2}{2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {\text {Chi}(b x)^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 9, normalized size = 0.90
method | result | size |
derivativedivides | \(\frac {\hyperbolicCosineIntegral \left (b x \right )^{2}}{2}\) | \(9\) |
default | \(\frac {\hyperbolicCosineIntegral \left (b x \right )^{2}}{2}\) | \(9\) |
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*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.22, size = 7, normalized size = 0.70 \begin {gather*} \frac {\operatorname {Chi}^{2}\left (b x\right )}{2} \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*} \text {could not integrate} \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 = -0.10 \begin {gather*} \frac {{\mathrm {coshint}\left (b\,x\right )}^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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