3.3.23 \(\int \frac {1}{(d x)^{3/2} (a+b \text {ArcCos}(c x))} \, dx\) [223]

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{(d x)^{3/2} (a+b \text {ArcCos}(c x))},x\right ) \]

[Out]

Unintegrable(1/(d*x)^(3/2)/(a+b*arccos(c*x)),x)

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Rubi [A]
time = 0.02, 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}{(d x)^{3/2} (a+b \text {ArcCos}(c x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/((d*x)^(3/2)*(a + b*ArcCos[c*x])),x]

[Out]

Defer[Int][1/((d*x)^(3/2)*(a + b*ArcCos[c*x])), x]

Rubi steps

\begin {align*} \int \frac {1}{(d x)^{3/2} \left (a+b \cos ^{-1}(c x)\right )} \, dx &=\int \frac {1}{(d x)^{3/2} \left (a+b \cos ^{-1}(c x)\right )} \, dx\\ \end {align*}

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Mathematica [A]
time = 2.39, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(d x)^{3/2} (a+b \text {ArcCos}(c x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/((d*x)^(3/2)*(a + b*ArcCos[c*x])),x]

[Out]

Integrate[1/((d*x)^(3/2)*(a + b*ArcCos[c*x])), x]

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Maple [A]
time = 0.22, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (d x \right )^{\frac {3}{2}} \left (a +b \arccos \left (c x \right )\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(d*x)^(3/2)/(a+b*arccos(c*x)),x)

[Out]

int(1/(d*x)^(3/2)/(a+b*arccos(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(1/(d*x)^(3/2)/(a+b*arccos(c*x)),x, algorithm="maxima")

[Out]

integrate(1/((d*x)^(3/2)*(b*arccos(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(1/(d*x)^(3/2)/(a+b*arccos(c*x)),x, algorithm="fricas")

[Out]

integral(sqrt(d*x)/(b*d^2*x^2*arccos(c*x) + a*d^2*x^2), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (d x\right )^{\frac {3}{2}} \left (a + b \operatorname {acos}{\left (c x \right )}\right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(d*x)**(3/2)/(a+b*acos(c*x)),x)

[Out]

Integral(1/((d*x)**(3/2)*(a + b*acos(c*x))), x)

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Giac [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(1/(d*x)^(3/2)/(a+b*arccos(c*x)),x, algorithm="giac")

[Out]

integrate(1/((d*x)^(3/2)*(b*arccos(c*x) + a)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {1}{\left (a+b\,\mathrm {acos}\left (c\,x\right )\right )\,{\left (d\,x\right )}^{3/2}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((a + b*acos(c*x))*(d*x)^(3/2)),x)

[Out]

int(1/((a + b*acos(c*x))*(d*x)^(3/2)), x)

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