3.3.21 \(\int \frac {\sqrt {d x}}{a+b \text {ArcCos}(c x)} \, dx\) [221]

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

[Out]

Unintegrable((d*x)^(1/2)/(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 {\sqrt {d x}}{a+b \text {ArcCos}(c x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Sqrt[d*x]/(a + b*ArcCos[c*x]),x]

[Out]

Defer[Int][Sqrt[d*x]/(a + b*ArcCos[c*x]), x]

Rubi steps

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

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Mathematica [A]
time = 1.91, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {d x}}{a+b \text {ArcCos}(c x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Sqrt[d*x]/(a + b*ArcCos[c*x]),x]

[Out]

Integrate[Sqrt[d*x]/(a + b*ArcCos[c*x]), x]

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Maple [A]
time = 0.24, size = 0, normalized size = 0.00 \[\int \frac {\sqrt {d x}}{a +b \arccos \left (c x \right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(sqrt(d*x)/(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((d*x)^(1/2)/(a+b*arccos(c*x)),x, algorithm="giac")

[Out]

integrate(sqrt(d*x)/(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 {\sqrt {d\,x}}{a+b\,\mathrm {acos}\left (c\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x)^(1/2)/(a + b*acos(c*x)),x)

[Out]

int((d*x)^(1/2)/(a + b*acos(c*x)), x)

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