3.1.48 \(\int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx\) [48]

Optimal. Leaf size=23 \[ \text {Int}\left ((c+d x)^m (a+a \tanh (e+f x))^2,x\right ) \]

[Out]

Unintegrable((d*x+c)^m*(a+a*tanh(f*x+e))^2,x)

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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 = {} \begin {gather*} \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(c + d*x)^m*(a + a*Tanh[e + f*x])^2,x]

[Out]

Defer[Int][(c + d*x)^m*(a + a*Tanh[e + f*x])^2, x]

Rubi steps

\begin {align*} \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx &=\int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx\\ \end {align*}

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Mathematica [A]
time = 22.58, size = 0, normalized size = 0.00 \begin {gather*} \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(c + d*x)^m*(a + a*Tanh[e + f*x])^2,x]

[Out]

Integrate[(c + d*x)^m*(a + a*Tanh[e + f*x])^2, x]

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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \left (d x +c \right )^{m} \left (a +a \tanh \left (f x +e \right )\right )^{2}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x+c)^m*(a+a*tanh(f*x+e))^2,x)

[Out]

int((d*x+c)^m*(a+a*tanh(f*x+e))^2,x)

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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.

[In]

integrate((d*x+c)^m*(a+a*tanh(f*x+e))^2,x, algorithm="maxima")

[Out]

(d*x + c)^(m + 1)*a^2/(d*(m + 1)) + integrate(2*(d*x + c)^m*a^2*(e^(f*x + e) - e^(-f*x - e))/(e^(f*x + e) + e^
(-f*x - e)) + (d*x + c)^m*a^2*(e^(f*x + e) - e^(-f*x - e))^2/(e^(f*x + e) + e^(-f*x - e))^2, x)

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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.

[In]

integrate((d*x+c)^m*(a+a*tanh(f*x+e))^2,x, algorithm="fricas")

[Out]

integral((a^2*tanh(f*x + e)^2 + 2*a^2*tanh(f*x + e) + a^2)*(d*x + c)^m, x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} a^{2} \left (\int 2 \left (c + d x\right )^{m} \tanh {\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m} \tanh ^{2}{\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m}\, dx\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)**m*(a+a*tanh(f*x+e))**2,x)

[Out]

a**2*(Integral(2*(c + d*x)**m*tanh(e + f*x), x) + Integral((c + d*x)**m*tanh(e + f*x)**2, x) + Integral((c + d
*x)**m, x))

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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.

[In]

integrate((d*x+c)^m*(a+a*tanh(f*x+e))^2,x, algorithm="giac")

[Out]

integrate((a*tanh(f*x + e) + a)^2*(d*x + c)^m, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int {\left (a+a\,\mathrm {tanh}\left (e+f\,x\right )\right )}^2\,{\left (c+d\,x\right )}^m \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + a*tanh(e + f*x))^2*(c + d*x)^m,x)

[Out]

int((a + a*tanh(e + f*x))^2*(c + d*x)^m, x)

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