Optimal. Leaf size=32 \[ \text {Int}\left (\frac {\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right ) \]
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Rubi [A]
time = 0.04, 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 \frac {\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx &=\int \frac {\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx\\ \end {align*}
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Mathematica [A]
time = 32.80, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\sinh \left (d x +c \right )}{\left (f x +e \right )^{2} \left (a +i a \sinh \left (d x +c \right )\right )}\, dx\]
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*} - \frac {2}{- i a d e^{2} - 2 i a d e f x - i a d f^{2} x^{2} + \left (a d e^{2} e^{c} + 2 a d e f x e^{c} + a d f^{2} x^{2} e^{c}\right ) e^{d x}} - \frac {i \left (\int \left (- \frac {4 i f}{e^{3} e^{c} e^{d x} - i e^{3} + 3 e^{2} f x e^{c} e^{d x} - 3 i e^{2} f x + 3 e f^{2} x^{2} e^{c} e^{d x} - 3 i e f^{2} x^{2} + f^{3} x^{3} e^{c} e^{d x} - i f^{3} x^{3}}\right )\, dx + \int \left (- \frac {i d e}{e^{3} e^{c} e^{d x} - i e^{3} + 3 e^{2} f x e^{c} e^{d x} - 3 i e^{2} f x + 3 e f^{2} x^{2} e^{c} e^{d x} - 3 i e f^{2} x^{2} + f^{3} x^{3} e^{c} e^{d x} - i f^{3} x^{3}}\right )\, dx + \int \left (- \frac {i d f x}{e^{3} e^{c} e^{d x} - i e^{3} + 3 e^{2} f x e^{c} e^{d x} - 3 i e^{2} f x + 3 e f^{2} x^{2} e^{c} e^{d x} - 3 i e f^{2} x^{2} + f^{3} x^{3} e^{c} e^{d x} - i f^{3} x^{3}}\right )\, dx + \int \frac {d e e^{c} e^{d x}}{e^{3} e^{c} e^{d x} - i e^{3} + 3 e^{2} f x e^{c} e^{d x} - 3 i e^{2} f x + 3 e f^{2} x^{2} e^{c} e^{d x} - 3 i e f^{2} x^{2} + f^{3} x^{3} e^{c} e^{d x} - i f^{3} x^{3}}\, dx + \int \frac {d f x e^{c} e^{d x}}{e^{3} e^{c} e^{d x} - i e^{3} + 3 e^{2} f x e^{c} e^{d x} - 3 i e^{2} f x + 3 e f^{2} x^{2} e^{c} e^{d x} - 3 i e f^{2} x^{2} + f^{3} x^{3} e^{c} e^{d x} - i f^{3} x^{3}}\, dx\right )}{a d} \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 = -0.03 \begin {gather*} \int \frac {\mathrm {sinh}\left (c+d\,x\right )}{{\left (e+f\,x\right )}^2\,\left (a+a\,\mathrm {sinh}\left (c+d\,x\right )\,1{}\mathrm {i}\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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