3.39 \(\int \frac {(d+e x)^m}{a+b \cosh ^{-1}(c x)} \, dx\)

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

[Out]

Unintegrable((e*x+d)^m/(a+b*arccosh(c*x)),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 = {} \[ \int \frac {(d+e x)^m}{a+b \cosh ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.39, size = 0, normalized size = 0.00 \[ \int \frac {(d+e x)^m}{a+b \cosh ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.64, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (e x + d\right )}^{m}}{b \operatorname {arcosh}\left (c x\right ) + a}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (e x + d\right )}^{m}}{b \operatorname {arcosh}\left (c x\right ) + a}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x+d)^m/(a+b*arccosh(c*x)),x, algorithm="giac")

[Out]

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

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maple [A]  time = 1.76, size = 0, normalized size = 0.00 \[ \int \frac {\left (e x +d \right )^{m}}{a +b \,\mathrm {arccosh}\left (c x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (e x + d\right )}^{m}}{b \operatorname {arcosh}\left (c x\right ) + a}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x+d)^m/(a+b*arccosh(c*x)),x, algorithm="maxima")

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\left (d+e\,x\right )}^m}{a+b\,\mathrm {acosh}\left (c\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d + e*x)^m/(a + b*acosh(c*x)),x)

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (d + e x\right )^{m}}{a + b \operatorname {acosh}{\left (c x \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral((d + e*x)**m/(a + b*acosh(c*x)), x)

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