3.1.33 \(\int \frac {x}{a+b \sec ^{-1}(c x)} \, dx\) [33]

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {x}{a+b \sec ^{-1}(c x)},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.01, 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 {x}{a+b \sec ^{-1}(c x)} \, dx \end {gather*}

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*}

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Mathematica [A]
time = 2.46, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{a+b \sec ^{-1}(c x)} \, dx \end {gather*}

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 = 0.58, size = 0, normalized size = 0.00 \[\int \frac {x}{a +b \,\mathrm {arcsec}\left (c x \right )}\, dx\]

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 = 0.00, 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(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 = 0.00, 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(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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{a + b \operatorname {asec}{\left (c x \right )}}\, dx \end {gather*}

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 [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: AttributeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: AttributeError >> type

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {x}{a+b\,\mathrm {acos}\left (\frac {1}{c\,x}\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x/(a + b*acos(1/(c*x))),x)

[Out]

int(x/(a + b*acos(1/(c*x))), x)

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