Optimal. Leaf size=25 \[ -\frac {\cosh (b x)}{x}-\frac {\text {Chi}(b x)}{x}+b \text {Shi}(b x) \]
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Rubi [A]
time = 0.03, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 4, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {6668, 12, 3378,
3379} \begin {gather*} -\frac {\text {Chi}(b x)}{x}+b \text {Shi}(b x)-\frac {\cosh (b x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 3378
Rule 3379
Rule 6668
Rubi steps
\begin {align*} \int \frac {\text {Chi}(b x)}{x^2} \, dx &=-\frac {\text {Chi}(b x)}{x}+b \int \frac {\cosh (b x)}{b x^2} \, dx\\ &=-\frac {\text {Chi}(b x)}{x}+\int \frac {\cosh (b x)}{x^2} \, dx\\ &=-\frac {\cosh (b x)}{x}-\frac {\text {Chi}(b x)}{x}+b \int \frac {\sinh (b x)}{x} \, dx\\ &=-\frac {\cosh (b x)}{x}-\frac {\text {Chi}(b x)}{x}+b \text {Shi}(b x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 25, normalized size = 1.00 \begin {gather*} -\frac {\cosh (b x)}{x}-\frac {\text {Chi}(b x)}{x}+b \text {Shi}(b x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.27, size = 32, normalized size = 1.28
method | result | size |
derivativedivides | \(b \left (-\frac {\hyperbolicCosineIntegral \left (b x \right )}{b x}-\frac {\cosh \left (b x \right )}{b x}+\hyperbolicSineIntegral \left (b x \right )\right )\) | \(32\) |
default | \(b \left (-\frac {\hyperbolicCosineIntegral \left (b x \right )}{b x}-\frac {\cosh \left (b x \right )}{b x}+\hyperbolicSineIntegral \left (b x \right )\right )\) | \(32\) |
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 [B] Leaf count of result is larger than twice the leaf count of optimal. 39 vs.
\(2 (19) = 38\).
time = 0.56, size = 39, normalized size = 1.56 \begin {gather*} \frac {b^{2} x {{}_{3}F_{4}\left (\begin {matrix} \frac {1}{2}, 1, 1 \\ \frac {3}{2}, \frac {3}{2}, 2, 2 \end {matrix}\middle | {\frac {b^{2} x^{2}}{4}} \right )}}{4} - \frac {\log {\left (b^{2} x^{2} \right )}}{2 x} - \frac {1}{x} - \frac {\gamma }{x} \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 = -0.04 \begin {gather*} \int \frac {\mathrm {coshint}\left (b\,x\right )}{x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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