3.1.30 \(\int \frac {\text {ArcCos}(a x)}{\sqrt {c+d x^2}} \, dx\) [30]

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

[Out]

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

Verification is not applicable to the result.

[In]

Int[ArcCos[a*x]/Sqrt[c + d*x^2],x]

[Out]

Defer[Int][ArcCos[a*x]/Sqrt[c + d*x^2], x]

Rubi steps

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

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Mathematica [A]
time = 1.55, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {ArcCos}(a x)}{\sqrt {c+d x^2}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[ArcCos[a*x]/Sqrt[c + d*x^2],x]

[Out]

Integrate[ArcCos[a*x]/Sqrt[c + d*x^2], x]

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Maple [A]
time = 0.72, size = 0, normalized size = 0.00 \[\int \frac {\arccos \left (a x \right )}{\sqrt {d \,x^{2}+c}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(acos(a*x)/(c + d*x^2)^(1/2),x)

[Out]

int(acos(a*x)/(c + d*x^2)^(1/2), x)

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