Optimal. Leaf size=48 \[ \frac {x^{1+m} \text {Chi}(a+b x)}{1+m}-\frac {b \text {Int}\left (\frac {x^{1+m} \cosh (a+b x)}{a+b x},x\right )}{1+m} \]
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Rubi [A]
time = 0.19, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int x^m \text {Chi}(a+b x) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int x^m \text {Chi}(a+b x) \, dx &=\frac {x^{1+m} \text {Chi}(a+b x)}{1+m}-\frac {b \int \frac {x^{1+m} \cosh (a+b x)}{a+b x} \, dx}{1+m}\\ \end {align*}
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Mathematica [A]
time = 6.78, size = 0, normalized size = 0.00 \begin {gather*} \int x^m \text {Chi}(a+b x) \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.13, size = 0, normalized size = 0.00 \[\int x^{m} \hyperbolicCosineIntegral \left (b x +a \right )\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
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 [A]
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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^{m} \operatorname {Chi}\left (a + b x\right )\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
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 [A]
time = 0.00, size = -1, normalized size = -0.02 \begin {gather*} \int x^m\,\mathrm {coshint}\left (a+b\,x\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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