3.3.1 \(\int \frac {1}{x (a+b \text {ArcCos}(c x))^{5/2}} \, dx\) [201]

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {1}{x (a+b \text {ArcCos}(c x))^{5/2}},x\right ) \]

[Out]

Unintegrable(1/x/(a+b*arccos(c*x))^(5/2),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 = {} \begin {gather*} \int \frac {1}{x (a+b \text {ArcCos}(c x))^{5/2}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/(x*(a + b*ArcCos[c*x])^(5/2)),x]

[Out]

Defer[Int][1/(x*(a + b*ArcCos[c*x])^(5/2)), x]

Rubi steps

\begin {align*} \int \frac {1}{x \left (a+b \cos ^{-1}(c x)\right )^{5/2}} \, dx &=\int \frac {1}{x \left (a+b \cos ^{-1}(c x)\right )^{5/2}} \, dx\\ \end {align*}

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Mathematica [A]
time = 2.95, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x (a+b \text {ArcCos}(c x))^{5/2}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/(x*(a + b*ArcCos[c*x])^(5/2)),x]

[Out]

Integrate[1/(x*(a + b*ArcCos[c*x])^(5/2)), x]

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Maple [A]
time = 0.23, size = 0, normalized size = 0.00 \[\int \frac {1}{x \left (a +b \arccos \left (c x \right )\right )^{\frac {5}{2}}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/(a+b*arccos(c*x))^(5/2),x)

[Out]

int(1/x/(a+b*arccos(c*x))^(5/2),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(1/x/(a+b*arccos(c*x))^(5/2),x, algorithm="maxima")

[Out]

integrate(1/((b*arccos(c*x) + a)^(5/2)*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*arccos(c*x))^(5/2),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \left (a + b \operatorname {acos}{\left (c x \right )}\right )^{\frac {5}{2}}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*acos(c*x))**(5/2),x)

[Out]

Integral(1/(x*(a + b*acos(c*x))**(5/2)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*arccos(c*x))^(5/2),x, algorithm="giac")

[Out]

Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(co
nst gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {1}{x\,{\left (a+b\,\mathrm {acos}\left (c\,x\right )\right )}^{5/2}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*(a + b*acos(c*x))^(5/2)),x)

[Out]

int(1/(x*(a + b*acos(c*x))^(5/2)), x)

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