3.304 \(\int \frac {(e+f x)^2}{(a+b \sin (c+\frac {d}{x}))^2} \, dx\)

Optimal. Leaf size=25 \[ \text {Int}\left (\frac {(e+f x)^2}{\left (a+b \sin \left (c+\frac {d}{x}\right )\right )^2},x\right ) \]

[Out]

Unintegrable((f*x+e)^2/(a+b*sin(c+d/x))^2,x)

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {(e+f x)^2}{\left (a+b \sin \left (c+\frac {d}{x}\right )\right )^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 126.31, size = 0, normalized size = 0.00 \[ \int \frac {(e+f x)^2}{\left (a+b \sin \left (c+\frac {d}{x}\right )\right )^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.73, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {f^{2} x^{2} + 2 \, e f x + e^{2}}{b^{2} \cos \left (\frac {c x + d}{x}\right )^{2} - 2 \, a b \sin \left (\frac {c x + d}{x}\right ) - a^{2} - b^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(-(f^2*x^2 + 2*e*f*x + e^2)/(b^2*cos((c*x + d)/x)^2 - 2*a*b*sin((c*x + d)/x) - a^2 - b^2), x)

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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maple [A]  time = 5.01, size = 0, normalized size = 0.00 \[ \int \frac {\left (f x +e \right )^{2}}{\left (a +b \sin \left (c +\frac {d}{x}\right )\right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((f*x+e)^2/(a+b*sin(c+d/x))^2,x)

[Out]

int((f*x+e)^2/(a+b*sin(c+d/x))^2,x)

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maxima [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (e+f\,x\right )}^2}{{\left (a+b\,\sin \left (c+\frac {d}{x}\right )\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((e + f*x)^2/(a + b*sin(c + d/x))^2,x)

[Out]

int((e + f*x)^2/(a + b*sin(c + d/x))^2, x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((f*x+e)**2/(a+b*sin(c+d/x))**2,x)

[Out]

Timed out

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