3.1.31 \(\int \frac {1}{(d+e x)^2 (a+b \cosh ^{-1}(c x))} \, dx\) [31]

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{(d+e x)^2 \left (a+b \cosh ^{-1}(c x)\right )},x\right ) \]

[Out]

Unintegrable(1/(e*x+d)^2/(a+b*arccosh(c*x)),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 = {} \begin {gather*} \int \frac {1}{(d+e x)^2 \left (a+b \cosh ^{-1}(c x)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.29, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(d+e x)^2 \left (a+b \cosh ^{-1}(c x)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {1}{\left (a+b\,\mathrm {acosh}\left (c\,x\right )\right )\,{\left (d+e\,x\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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