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

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {1}{x \left (a+b \sec ^{-1}(c x)\right )},x\right ) \]

[Out]

Unintegrable(1/x/(a+b*arcsec(c*x)),x)

________________________________________________________________________________________

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

Verification is Not applicable to the result.

[In]

Int[1/(x*(a + b*ArcSec[c*x])),x]

[Out]

Defer[Int][1/(x*(a + b*ArcSec[c*x])), x]

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]  time = 0.29, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a+b \sec ^{-1}(c x)\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*(a + b*ArcSec[c*x])),x]

[Out]

Integrate[1/(x*(a + b*ArcSec[c*x])), x]

________________________________________________________________________________________

fricas [A]  time = 0.52, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{b x \operatorname {arcsec}\left (c x\right ) + a x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*arcsec(c*x)),x, algorithm="fricas")

[Out]

integral(1/(b*x*arcsec(c*x) + a*x), x)

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b \operatorname {arcsec}\left (c x\right ) + a\right )} x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*arcsec(c*x)),x, algorithm="giac")

[Out]

integrate(1/((b*arcsec(c*x) + a)*x), x)

________________________________________________________________________________________

maple [A]  time = 0.92, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a +b \,\mathrm {arcsec}\left (c x \right )\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/(a+b*arcsec(c*x)),x)

[Out]

int(1/x/(a+b*arcsec(c*x)),x)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b \operatorname {arcsec}\left (c x\right ) + a\right )} x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*arcsec(c*x)),x, algorithm="maxima")

[Out]

integrate(1/((b*arcsec(c*x) + a)*x), x)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {1}{x\,\left (a+b\,\mathrm {acos}\left (\frac {1}{c\,x}\right )\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*(a + b*acos(1/(c*x)))),x)

[Out]

int(1/(x*(a + b*acos(1/(c*x)))), x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a + b \operatorname {asec}{\left (c x \right )}\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*asec(c*x)),x)

[Out]

Integral(1/(x*(a + b*asec(c*x))), x)

________________________________________________________________________________________