Optimal. Leaf size=591 \[ -\frac {2 f x \text {ArcTan}\left (e^{c+d x}\right )}{a d}+\frac {2 b^2 (e+f x) \text {ArcTan}\left (e^{c+d x}\right )}{a \left (a^2+b^2\right ) d}+\frac {f x \text {ArcTan}(\sinh (c+d x))}{a d}-\frac {(e+f x) \text {ArcTan}(\sinh (c+d x))}{a d}+\frac {2 b (e+f x) \tanh ^{-1}\left (e^{2 c+2 d x}\right )}{a^2 d}-\frac {f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac {(e+f x) \text {csch}(c+d x)}{a d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}-\frac {b^3 (e+f x) \log \left (1+e^{2 (c+d x)}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {i f \text {PolyLog}\left (2,-i e^{c+d x}\right )}{a d^2}-\frac {i b^2 f \text {PolyLog}\left (2,-i e^{c+d x}\right )}{a \left (a^2+b^2\right ) d^2}-\frac {i f \text {PolyLog}\left (2,i e^{c+d x}\right )}{a d^2}+\frac {i b^2 f \text {PolyLog}\left (2,i e^{c+d x}\right )}{a \left (a^2+b^2\right ) d^2}+\frac {b^3 f \text {PolyLog}\left (2,-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d^2}+\frac {b^3 f \text {PolyLog}\left (2,-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d^2}-\frac {b^3 f \text {PolyLog}\left (2,-e^{2 (c+d x)}\right )}{2 a^2 \left (a^2+b^2\right ) d^2}+\frac {b f \text {PolyLog}\left (2,-e^{2 c+2 d x}\right )}{2 a^2 d^2}-\frac {b f \text {PolyLog}\left (2,e^{2 c+2 d x}\right )}{2 a^2 d^2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.62, antiderivative size = 591, normalized size of antiderivative = 1.00, number of steps
used = 37, number of rules used = 18, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.562, Rules used = {5708, 2701,
327, 213, 5570, 5311, 12, 4265, 2317, 2438, 3855, 5569, 4267, 5692, 5680, 2221, 6874, 3799}
\begin {gather*} \frac {2 b^2 (e+f x) \text {ArcTan}\left (e^{c+d x}\right )}{a d \left (a^2+b^2\right )}-\frac {i b^2 f \text {Li}_2\left (-i e^{c+d x}\right )}{a d^2 \left (a^2+b^2\right )}+\frac {i b^2 f \text {Li}_2\left (i e^{c+d x}\right )}{a d^2 \left (a^2+b^2\right )}+\frac {b^3 f \text {Li}_2\left (-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d^2 \left (a^2+b^2\right )}+\frac {b^3 f \text {Li}_2\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 d^2 \left (a^2+b^2\right )}-\frac {b^3 f \text {Li}_2\left (-e^{2 (c+d x)}\right )}{2 a^2 d^2 \left (a^2+b^2\right )}+\frac {b^3 (e+f x) \log \left (\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}+1\right )}{a^2 d \left (a^2+b^2\right )}+\frac {b^3 (e+f x) \log \left (\frac {b e^{c+d x}}{\sqrt {a^2+b^2}+a}+1\right )}{a^2 d \left (a^2+b^2\right )}-\frac {b^3 (e+f x) \log \left (e^{2 (c+d x)}+1\right )}{a^2 d \left (a^2+b^2\right )}+\frac {b f \text {Li}_2\left (-e^{2 c+2 d x}\right )}{2 a^2 d^2}-\frac {b f \text {Li}_2\left (e^{2 c+2 d x}\right )}{2 a^2 d^2}+\frac {2 b (e+f x) \tanh ^{-1}\left (e^{2 c+2 d x}\right )}{a^2 d}-\frac {(e+f x) \text {ArcTan}(\sinh (c+d x))}{a d}-\frac {2 f x \text {ArcTan}\left (e^{c+d x}\right )}{a d}+\frac {f x \text {ArcTan}(\sinh (c+d x))}{a d}+\frac {i f \text {Li}_2\left (-i e^{c+d x}\right )}{a d^2}-\frac {i f \text {Li}_2\left (i e^{c+d x}\right )}{a d^2}-\frac {f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac {(e+f x) \text {csch}(c+d x)}{a d} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 213
Rule 327
Rule 2221
Rule 2317
Rule 2438
Rule 2701
Rule 3799
Rule 3855
Rule 4265
Rule 4267
Rule 5311
Rule 5569
Rule 5570
Rule 5680
Rule 5692
Rule 5708
Rule 6874
Rubi steps
\begin {align*} \int \frac {(e+f x) \text {csch}^2(c+d x) \text {sech}(c+d x)}{a+b \sinh (c+d x)} \, dx &=\frac {\int (e+f x) \text {csch}^2(c+d x) \text {sech}(c+d x) \, dx}{a}-\frac {b \int \frac {(e+f x) \text {csch}(c+d x) \text {sech}(c+d x)}{a+b \sinh (c+d x)} \, dx}{a}\\ &=-\frac {(e+f x) \tan ^{-1}(\sinh (c+d x))}{a d}-\frac {(e+f x) \text {csch}(c+d x)}{a d}-\frac {b \int (e+f x) \text {csch}(c+d x) \text {sech}(c+d x) \, dx}{a^2}+\frac {b^2 \int \frac {(e+f x) \text {sech}(c+d x)}{a+b \sinh (c+d x)} \, dx}{a^2}-\frac {f \int \left (-\frac {\tan ^{-1}(\sinh (c+d x))}{d}-\frac {\text {csch}(c+d x)}{d}\right ) \, dx}{a}\\ &=-\frac {(e+f x) \tan ^{-1}(\sinh (c+d x))}{a d}-\frac {(e+f x) \text {csch}(c+d x)}{a d}-\frac {(2 b) \int (e+f x) \text {csch}(2 c+2 d x) \, dx}{a^2}+\frac {b^2 \int (e+f x) \text {sech}(c+d x) (a-b \sinh (c+d x)) \, dx}{a^2 \left (a^2+b^2\right )}+\frac {b^4 \int \frac {(e+f x) \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx}{a^2 \left (a^2+b^2\right )}+\frac {f \int \tan ^{-1}(\sinh (c+d x)) \, dx}{a d}+\frac {f \int \text {csch}(c+d x) \, dx}{a d}\\ &=-\frac {b^3 (e+f x)^2}{2 a^2 \left (a^2+b^2\right ) f}+\frac {f x \tan ^{-1}(\sinh (c+d x))}{a d}-\frac {(e+f x) \tan ^{-1}(\sinh (c+d x))}{a d}+\frac {2 b (e+f x) \tanh ^{-1}\left (e^{2 c+2 d x}\right )}{a^2 d}-\frac {f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac {(e+f x) \text {csch}(c+d x)}{a d}+\frac {b^2 \int (a (e+f x) \text {sech}(c+d x)-b (e+f x) \tanh (c+d x)) \, dx}{a^2 \left (a^2+b^2\right )}+\frac {b^4 \int \frac {e^{c+d x} (e+f x)}{a-\sqrt {a^2+b^2}+b e^{c+d x}} \, dx}{a^2 \left (a^2+b^2\right )}+\frac {b^4 \int \frac {e^{c+d x} (e+f x)}{a+\sqrt {a^2+b^2}+b e^{c+d x}} \, dx}{a^2 \left (a^2+b^2\right )}-\frac {f \int d x \text {sech}(c+d x) \, dx}{a d}+\frac {(b f) \int \log \left (1-e^{2 c+2 d x}\right ) \, dx}{a^2 d}-\frac {(b f) \int \log \left (1+e^{2 c+2 d x}\right ) \, dx}{a^2 d}\\ &=-\frac {b^3 (e+f x)^2}{2 a^2 \left (a^2+b^2\right ) f}+\frac {f x \tan ^{-1}(\sinh (c+d x))}{a d}-\frac {(e+f x) \tan ^{-1}(\sinh (c+d x))}{a d}+\frac {2 b (e+f x) \tanh ^{-1}\left (e^{2 c+2 d x}\right )}{a^2 d}-\frac {f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac {(e+f x) \text {csch}(c+d x)}{a d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {b^2 \int (e+f x) \text {sech}(c+d x) \, dx}{a \left (a^2+b^2\right )}-\frac {b^3 \int (e+f x) \tanh (c+d x) \, dx}{a^2 \left (a^2+b^2\right )}-\frac {f \int x \text {sech}(c+d x) \, dx}{a}+\frac {(b f) \text {Subst}\left (\int \frac {\log (1-x)}{x} \, dx,x,e^{2 c+2 d x}\right )}{2 a^2 d^2}-\frac {(b f) \text {Subst}\left (\int \frac {\log (1+x)}{x} \, dx,x,e^{2 c+2 d x}\right )}{2 a^2 d^2}-\frac {\left (b^3 f\right ) \int \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right ) \, dx}{a^2 \left (a^2+b^2\right ) d}-\frac {\left (b^3 f\right ) \int \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right ) \, dx}{a^2 \left (a^2+b^2\right ) d}\\ &=-\frac {2 f x \tan ^{-1}\left (e^{c+d x}\right )}{a d}+\frac {2 b^2 (e+f x) \tan ^{-1}\left (e^{c+d x}\right )}{a \left (a^2+b^2\right ) d}+\frac {f x \tan ^{-1}(\sinh (c+d x))}{a d}-\frac {(e+f x) \tan ^{-1}(\sinh (c+d x))}{a d}+\frac {2 b (e+f x) \tanh ^{-1}\left (e^{2 c+2 d x}\right )}{a^2 d}-\frac {f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac {(e+f x) \text {csch}(c+d x)}{a d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {b f \text {Li}_2\left (-e^{2 c+2 d x}\right )}{2 a^2 d^2}-\frac {b f \text {Li}_2\left (e^{2 c+2 d x}\right )}{2 a^2 d^2}-\frac {\left (2 b^3\right ) \int \frac {e^{2 (c+d x)} (e+f x)}{1+e^{2 (c+d x)}} \, dx}{a^2 \left (a^2+b^2\right )}-\frac {\left (b^3 f\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{a-\sqrt {a^2+b^2}}\right )}{x} \, dx,x,e^{c+d x}\right )}{a^2 \left (a^2+b^2\right ) d^2}-\frac {\left (b^3 f\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{a+\sqrt {a^2+b^2}}\right )}{x} \, dx,x,e^{c+d x}\right )}{a^2 \left (a^2+b^2\right ) d^2}+\frac {(i f) \int \log \left (1-i e^{c+d x}\right ) \, dx}{a d}-\frac {(i f) \int \log \left (1+i e^{c+d x}\right ) \, dx}{a d}-\frac {\left (i b^2 f\right ) \int \log \left (1-i e^{c+d x}\right ) \, dx}{a \left (a^2+b^2\right ) d}+\frac {\left (i b^2 f\right ) \int \log \left (1+i e^{c+d x}\right ) \, dx}{a \left (a^2+b^2\right ) d}\\ &=-\frac {2 f x \tan ^{-1}\left (e^{c+d x}\right )}{a d}+\frac {2 b^2 (e+f x) \tan ^{-1}\left (e^{c+d x}\right )}{a \left (a^2+b^2\right ) d}+\frac {f x \tan ^{-1}(\sinh (c+d x))}{a d}-\frac {(e+f x) \tan ^{-1}(\sinh (c+d x))}{a d}+\frac {2 b (e+f x) \tanh ^{-1}\left (e^{2 c+2 d x}\right )}{a^2 d}-\frac {f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac {(e+f x) \text {csch}(c+d x)}{a d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}-\frac {b^3 (e+f x) \log \left (1+e^{2 (c+d x)}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {b^3 f \text {Li}_2\left (-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d^2}+\frac {b^3 f \text {Li}_2\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d^2}+\frac {b f \text {Li}_2\left (-e^{2 c+2 d x}\right )}{2 a^2 d^2}-\frac {b f \text {Li}_2\left (e^{2 c+2 d x}\right )}{2 a^2 d^2}+\frac {(i f) \text {Subst}\left (\int \frac {\log (1-i x)}{x} \, dx,x,e^{c+d x}\right )}{a d^2}-\frac {(i f) \text {Subst}\left (\int \frac {\log (1+i x)}{x} \, dx,x,e^{c+d x}\right )}{a d^2}-\frac {\left (i b^2 f\right ) \text {Subst}\left (\int \frac {\log (1-i x)}{x} \, dx,x,e^{c+d x}\right )}{a \left (a^2+b^2\right ) d^2}+\frac {\left (i b^2 f\right ) \text {Subst}\left (\int \frac {\log (1+i x)}{x} \, dx,x,e^{c+d x}\right )}{a \left (a^2+b^2\right ) d^2}+\frac {\left (b^3 f\right ) \int \log \left (1+e^{2 (c+d x)}\right ) \, dx}{a^2 \left (a^2+b^2\right ) d}\\ &=-\frac {2 f x \tan ^{-1}\left (e^{c+d x}\right )}{a d}+\frac {2 b^2 (e+f x) \tan ^{-1}\left (e^{c+d x}\right )}{a \left (a^2+b^2\right ) d}+\frac {f x \tan ^{-1}(\sinh (c+d x))}{a d}-\frac {(e+f x) \tan ^{-1}(\sinh (c+d x))}{a d}+\frac {2 b (e+f x) \tanh ^{-1}\left (e^{2 c+2 d x}\right )}{a^2 d}-\frac {f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac {(e+f x) \text {csch}(c+d x)}{a d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}-\frac {b^3 (e+f x) \log \left (1+e^{2 (c+d x)}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {i f \text {Li}_2\left (-i e^{c+d x}\right )}{a d^2}-\frac {i b^2 f \text {Li}_2\left (-i e^{c+d x}\right )}{a \left (a^2+b^2\right ) d^2}-\frac {i f \text {Li}_2\left (i e^{c+d x}\right )}{a d^2}+\frac {i b^2 f \text {Li}_2\left (i e^{c+d x}\right )}{a \left (a^2+b^2\right ) d^2}+\frac {b^3 f \text {Li}_2\left (-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d^2}+\frac {b^3 f \text {Li}_2\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d^2}+\frac {b f \text {Li}_2\left (-e^{2 c+2 d x}\right )}{2 a^2 d^2}-\frac {b f \text {Li}_2\left (e^{2 c+2 d x}\right )}{2 a^2 d^2}+\frac {\left (b^3 f\right ) \text {Subst}\left (\int \frac {\log (1+x)}{x} \, dx,x,e^{2 (c+d x)}\right )}{2 a^2 \left (a^2+b^2\right ) d^2}\\ &=-\frac {2 f x \tan ^{-1}\left (e^{c+d x}\right )}{a d}+\frac {2 b^2 (e+f x) \tan ^{-1}\left (e^{c+d x}\right )}{a \left (a^2+b^2\right ) d}+\frac {f x \tan ^{-1}(\sinh (c+d x))}{a d}-\frac {(e+f x) \tan ^{-1}(\sinh (c+d x))}{a d}+\frac {2 b (e+f x) \tanh ^{-1}\left (e^{2 c+2 d x}\right )}{a^2 d}-\frac {f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac {(e+f x) \text {csch}(c+d x)}{a d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {b^3 (e+f x) \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d}-\frac {b^3 (e+f x) \log \left (1+e^{2 (c+d x)}\right )}{a^2 \left (a^2+b^2\right ) d}+\frac {i f \text {Li}_2\left (-i e^{c+d x}\right )}{a d^2}-\frac {i b^2 f \text {Li}_2\left (-i e^{c+d x}\right )}{a \left (a^2+b^2\right ) d^2}-\frac {i f \text {Li}_2\left (i e^{c+d x}\right )}{a d^2}+\frac {i b^2 f \text {Li}_2\left (i e^{c+d x}\right )}{a \left (a^2+b^2\right ) d^2}+\frac {b^3 f \text {Li}_2\left (-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d^2}+\frac {b^3 f \text {Li}_2\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 \left (a^2+b^2\right ) d^2}-\frac {b^3 f \text {Li}_2\left (-e^{2 (c+d x)}\right )}{2 a^2 \left (a^2+b^2\right ) d^2}+\frac {b f \text {Li}_2\left (-e^{2 c+2 d x}\right )}{2 a^2 d^2}-\frac {b f \text {Li}_2\left (e^{2 c+2 d x}\right )}{2 a^2 d^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 5.38, size = 591, normalized size = 1.00 \begin {gather*} \frac {-\frac {d (e+f x) \coth \left (\frac {1}{2} (c+d x)\right )}{a}-\frac {2 b d e \log (\sinh (c+d x))}{a^2}+\frac {2 b c f \log (\sinh (c+d x))}{a^2}+\frac {2 f \log \left (\tanh \left (\frac {1}{2} (c+d x)\right )\right )}{a}+\frac {b f \left (-\left ((c+d x) \left (c+d x+2 \log \left (1-e^{-2 (c+d x)}\right )\right )\right )+\text {PolyLog}\left (2,e^{-2 (c+d x)}\right )\right )}{a^2}+\frac {2 b^3 \left (-\frac {1}{2} f (c+d x)^2+f (c+d x) \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )+f (c+d x) \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))+f \text {PolyLog}\left (2,\frac {b e^{c+d x}}{-a+\sqrt {a^2+b^2}}\right )+f \text {PolyLog}\left (2,-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )\right )}{a^2 \left (a^2+b^2\right )}+\frac {2 \left (-b d e (c+d x)+b c f (c+d x)+\frac {1}{2} b f (c+d x)^2-2 a d e \text {ArcTan}(\cosh (c+d x)+\sinh (c+d x))+2 a c f \text {ArcTan}(\cosh (c+d x)+\sinh (c+d x))-2 a f (c+d x) \text {ArcTan}(\cosh (c+d x)+\sinh (c+d x))+b f (c+d x) \log (2 \cosh (c+d x) (\cosh (c+d x)-\sinh (c+d x)))+b d e \log (1+\cosh (2 (c+d x))+\sinh (2 (c+d x)))-b c f \log (1+\cosh (2 (c+d x))+\sinh (2 (c+d x)))+i a f \text {PolyLog}(2,-i (\cosh (c+d x)+\sinh (c+d x)))-i a f \text {PolyLog}(2,i (\cosh (c+d x)+\sinh (c+d x)))-\frac {1}{2} b f \text {PolyLog}(2,-\cosh (2 (c+d x))+\sinh (2 (c+d x)))\right )}{a^2+b^2}+\frac {d (e+f x) \tanh \left (\frac {1}{2} (c+d x)\right )}{a}}{2 d^2} \end {gather*}
Warning: Unable to verify antiderivative.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Both result and optimal contain complex but leaf count of result is larger than twice
the leaf count of optimal. 1528 vs. \(2 (556 ) = 1112\).
time = 5.84, size = 1529, normalized size = 2.59
method | result | size |
risch | \(\text {Expression too large to display}\) | \(1529\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Both result and optimal contain complex but leaf count of result is larger than twice
the leaf count of optimal. 2955 vs. \(2 (546) = 1092\).
time = 0.52, size = 2955, normalized size = 5.00 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {e+f\,x}{\mathrm {cosh}\left (c+d\,x\right )\,{\mathrm {sinh}\left (c+d\,x\right )}^2\,\left (a+b\,\mathrm {sinh}\left (c+d\,x\right )\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________