### 3.362 $$\int x^m \tanh ^2(a+b x) \, dx$$

Optimal. Leaf size=14 $\text{Unintegrable}\left (x^m \tanh ^2(a+b x),x\right )$

[Out]

Unintegrable[x^m*Tanh[a + b*x]^2, x]

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Rubi [A]  time = 0.0318242, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0., Rules used = {} $\int x^m \tanh ^2(a+b x) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[x^m*Tanh[a + b*x]^2,x]

[Out]

Defer[Int][x^m*Tanh[a + b*x]^2, x]

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 = 0.584517, size = 0, normalized size = 0. $\int x^m \tanh ^2(a+b x) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[x^m*Tanh[a + b*x]^2,x]

[Out]

Integrate[x^m*Tanh[a + b*x]^2, x]

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Maple [A]  time = 0.059, size = 0, normalized size = 0. \begin{align*} \int{x}^{m} \left ({\rm sech} \left (bx+a\right ) \right ) ^{2} \left ( \sinh \left ( bx+a \right ) \right ) ^{2}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*sech(b*x+a)^2*sinh(b*x+a)^2,x)

[Out]

int(x^m*sech(b*x+a)^2*sinh(b*x+a)^2,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \frac{x e^{\left (4 \, b x + m \log \left (x\right ) + 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} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*sech(b*x+a)^2*sinh(b*x+a)^2,x, algorithm="maxima")

[Out]

x*e^(4*b*x + m*log(x) + 4*a)/((m + 1)*e^(4*b*x + 4*a) + 2*(m + 1)*e^(2*b*x + 2*a) + m + 1) - integrate((2*(2*b
*x*e^(4*a) + (m + 1)*e^(4*a))*e^(4*b*x) + (m + 1)*e^(2*b*x + 2*a) - m - 1)*x^m/((m + 1)*e^(6*b*x + 6*a) + 3*(m
+ 1)*e^(4*b*x + 4*a) + 3*(m + 1)*e^(2*b*x + 2*a) + m + 1), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (x^{m} \operatorname{sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{2}, x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*sech(b*x+a)^2*sinh(b*x+a)^2,x, algorithm="fricas")

[Out]

integral(x^m*sech(b*x + a)^2*sinh(b*x + a)^2, x)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m*sech(b*x+a)**2*sinh(b*x+a)**2,x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{m} \operatorname{sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{2}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*sech(b*x+a)^2*sinh(b*x+a)^2,x, algorithm="giac")

[Out]

integrate(x^m*sech(b*x + a)^2*sinh(b*x + a)^2, x)