3.5 \(\int \frac {\tanh (e+f x)}{(c+d x)^2} \, dx\)

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {\tanh (e+f x)}{(c+d x)^2},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.02, 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 = {} \[ \int \frac {\tanh (e+f x)}{(c+d x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Tanh[e + f*x]/(c + d*x)^2,x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 16.81, size = 0, normalized size = 0.00 \[ \int \frac {\tanh (e+f x)}{(c+d x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.51, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\tanh \left (f x + e\right )}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.22, size = 0, normalized size = 0.00 \[ \int \frac {\tanh \left (f x +e \right )}{\left (d x +c \right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {1}{d^{2} x + c d} - 2 \, \int \frac {1}{d^{2} x^{2} + 2 \, c d x + c^{2} + {\left (d^{2} x^{2} e^{\left (2 \, e\right )} + 2 \, c d x e^{\left (2 \, e\right )} + c^{2} e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {\mathrm {tanh}\left (e+f\,x\right )}{{\left (c+d\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(tanh(e + f*x)/(c + d*x)^2,x)

[Out]

int(tanh(e + f*x)/(c + d*x)^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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