Optimal. Leaf size=15 \[ \text {Int}\left (x^m \tanh ^2(a+b x),x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, 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 = {} \[ \int x^m \tanh ^2(a+b x) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int x^m \tanh ^2(a+b x) \, dx &=\int x^m \tanh ^2(a+b x) \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.62, size = 0, normalized size = 0.00 \[ \int x^m \tanh ^2(a+b x) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.54, size = 0, normalized size = 0.00 \[ {\rm integral}\left (x^{m} \operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{2}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{m} \operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.28, size = 0, normalized size = 0.00 \[ \int x^{m} \mathrm {sech}\left (b x +a \right )^{2} \left (\sinh ^{2}\left (b x +a \right )\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {x e^{\left (4 \, b x + m \log \relax (x) + 4 \, a\right )}}{{\left (m + 1\right )} e^{\left (4 \, b x + 4 \, a\right )} + 2 \, {\left (m + 1\right )} e^{\left (2 \, b x + 2 \, a\right )} + m + 1} - \int \frac {{\left (2 \, {\left (2 \, b x e^{\left (4 \, a\right )} + {\left (m + 1\right )} e^{\left (4 \, a\right )}\right )} e^{\left (4 \, b x\right )} + {\left (m + 1\right )} e^{\left (2 \, b x + 2 \, a\right )} - m - 1\right )} x^{m}}{{\left (m + 1\right )} e^{\left (6 \, b x + 6 \, a\right )} + 3 \, {\left (m + 1\right )} e^{\left (4 \, b x + 4 \, a\right )} + 3 \, {\left (m + 1\right )} e^{\left (2 \, b x + 2 \, a\right )} + m + 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {x^m\,{\mathrm {sinh}\left (a+b\,x\right )}^2}{{\mathrm {cosh}\left (a+b\,x\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________