3.7.71 \(\int \frac {1}{(d+e x^2) (a+b \text {ArcSin}(c x))} \, dx\) [671]

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {1}{\left (d+e x^2\right ) (a+b \text {ArcSin}(c x))},x\right ) \]

[Out]

Unintegrable(1/(e*x^2+d)/(a+b*arcsin(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}{\left (d+e x^2\right ) (a+b \text {ArcSin}(c x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.50, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (d+e x^2\right ) (a+b \text {ArcSin}(c x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.95, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (e \,x^{2}+d \right ) \left (a +b \arcsin \left (c x \right )\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

integral(1/(a*x^2*e + a*d + (b*x^2*e + b*d)*arcsin(c*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(1/((a + b*asin(c*x))*(d + e*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(1/(e*x^2+d)/(a+b*arcsin(c*x)),x, algorithm="giac")

[Out]

integrate(1/((e*x^2 + d)*(b*arcsin(c*x) + a)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {1}{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )\,\left (e\,x^2+d\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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