3.25 \(\int \frac{1}{(d+e x) (a+b \sin ^{-1}(c x))^2} \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{1}{(d+e x) \left (a+b \sin ^{-1}(c x)\right )^2},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.028645, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{1}{(d+e x) \left (a+b \sin ^{-1}(c x)\right )^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 6.10365, size = 0, normalized size = 0. \[ \int \frac{1}{(d+e x) \left (a+b \sin ^{-1}(c x)\right )^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 3.938, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( ex+d \right ) \left ( a+b\arcsin \left ( cx \right ) \right ) ^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{a^{2} e x + a^{2} d +{\left (b^{2} e x + b^{2} d\right )} \arcsin \left (c x\right )^{2} + 2 \,{\left (a b e x + a b d\right )} \arcsin \left (c x\right )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (e x + d\right )}{\left (b \arcsin \left (c x\right ) + a\right )}^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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