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

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{(d+e x)^m}{a+b \sinh ^{-1}(c x)},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0289984, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{(d+e x)^m}{a+b \sinh ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.341616, size = 0, normalized size = 0. \[ \int \frac{(d+e x)^m}{a+b \sinh ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.891, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( ex+d \right ) ^{m}}{a+b{\it Arcsinh} \left ( cx \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (e x + d\right )}^{m}}{b \operatorname{arsinh}\left (c x\right ) + a}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{{\left (e x + d\right )}^{m}}{b \operatorname{arsinh}\left (c x\right ) + a}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (d + e x\right )^{m}}{a + b \operatorname{asinh}{\left (c x \right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (e x + d\right )}^{m}}{b \operatorname{arsinh}\left (c x\right ) + a}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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