3.1.72 \(\int \frac {1}{(c+d x)^2 (a+b \tanh (e+f x))} \, dx\) [72]

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {1}{(c+d x)^2 (a+b \tanh (e+f x))},x\right ) \]

[Out]

Unintegrable(1/(d*x+c)^2/(a+b*tanh(f*x+e)),x)

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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 {1}{(c+d x)^2 (a+b \tanh (e+f x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/((c + d*x)^2*(a + b*Tanh[e + f*x])),x]

[Out]

Defer[Int][1/((c + d*x)^2*(a + b*Tanh[e + f*x])), x]

Rubi steps

\begin {align*} \int \frac {1}{(c+d x)^2 (a+b \tanh (e+f x))} \, dx &=\int \frac {1}{(c+d x)^2 (a+b \tanh (e+f x))} \, dx\\ \end {align*}

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Mathematica [A]
time = 15.59, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(c+d x)^2 (a+b \tanh (e+f x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/((c + d*x)^2*(a + b*Tanh[e + f*x])),x]

[Out]

Integrate[1/((c + d*x)^2*(a + b*Tanh[e + f*x])), x]

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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (d x +c \right )^{2} \left (a +b \tanh \left (f x +e \right )\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(d*x+c)^2/(a+b*tanh(f*x+e)),x)

[Out]

int(1/(d*x+c)^2/(a+b*tanh(f*x+e)),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(1/(d*x+c)^2/(a+b*tanh(f*x+e)),x, algorithm="maxima")

[Out]

2*b*integrate(1/(a^2*c^2 - b^2*c^2 + (a^2*d^2 - b^2*d^2)*x^2 + 2*(a^2*c*d - b^2*c*d)*x + ((a^2*d^2 + 2*a*b*d^2
+ b^2*d^2)*x^2*e^(2*e) + 2*(a^2*c*d + 2*a*b*c*d + b^2*c*d)*x*e^(2*e) + (a^2*c^2 + 2*a*b*c^2 + b^2*c^2)*e^(2*e
))*e^(2*f*x)), x) - 1/(a*c*d + b*c*d + (a*d^2 + b*d^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(1/(d*x+c)^2/(a+b*tanh(f*x+e)),x, algorithm="fricas")

[Out]

integral(1/(a*d^2*x^2 + 2*a*c*d*x + a*c^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*tanh(f*x + e)), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (a + b \tanh {\left (e + f x \right )}\right ) \left (c + d x\right )^{2}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(d*x+c)**2/(a+b*tanh(f*x+e)),x)

[Out]

Integral(1/((a + b*tanh(e + f*x))*(c + d*x)**2), 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(1/(d*x+c)^2/(a+b*tanh(f*x+e)),x, algorithm="giac")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((a + b*tanh(e + f*x))*(c + d*x)^2),x)

[Out]

int(1/((a + b*tanh(e + f*x))*(c + d*x)^2), x)

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