3.33 \(\int \frac{x}{a+b \sec ^{-1}(c x)} \, dx\)

Optimal. Leaf size=14 \[ \text{Unintegrable}\left (\frac{x}{a+b \sec ^{-1}(c x)},x\right ) \]

[Out]

Unintegrable[x/(a + b*ArcSec[c*x]), x]

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Rubi [A]  time = 0.0144259, 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 = {} \[ \int \frac{x}{a+b \sec ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[x/(a + b*ArcSec[c*x]),x]

[Out]

Defer[Int][x/(a + b*ArcSec[c*x]), x]

Rubi steps

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

Mathematica [A]  time = 2.55557, size = 0, normalized size = 0. \[ \int \frac{x}{a+b \sec ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x/(a + b*ArcSec[c*x]),x]

[Out]

Integrate[x/(a + b*ArcSec[c*x]), x]

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Maple [A]  time = 0.973, size = 0, normalized size = 0. \begin{align*} \int{\frac{x}{a+b{\rm arcsec} \left (cx\right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x/(a+b*arcsec(c*x)),x)

[Out]

int(x/(a+b*arcsec(c*x)),x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(a+b*arcsec(c*x)),x, algorithm="maxima")

[Out]

integrate(x/(b*arcsec(c*x) + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(a+b*arcsec(c*x)),x, algorithm="fricas")

[Out]

integral(x/(b*arcsec(c*x) + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(a+b*asec(c*x)),x)

[Out]

Integral(x/(a + b*asec(c*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(a+b*arcsec(c*x)),x, algorithm="giac")

[Out]

integrate(x/(b*arcsec(c*x) + a), x)