3.909 \(\int F(\frac {x^2}{(a+b x)^2}) \, dx\)

Optimal. Leaf size=15 \[ \text {Int}\left (F\left (\frac {x^2}{(a+b x)^2}\right ),x\right ) \]

[Out]

CannotIntegrate(F(x^2/(b*x+a)^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 = {} \[ \int F\left (\frac {x^2}{(a+b x)^2}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Int[F[x^2/(a + b*x)^2],x]

[Out]

Defer[Int][F[x^2/(a + b*x)^2], x]

Rubi steps

\begin {align*} \int F\left (\frac {x^2}{(a+b x)^2}\right ) \, dx &=\int F\left (\frac {x^2}{(a+b x)^2}\right ) \, dx\\ \end {align*}

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Mathematica [A]  time = 0.01, size = 0, normalized size = 0.00 \[ \int F\left (\frac {x^2}{(a+b x)^2}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[F[x^2/(a + b*x)^2],x]

[Out]

Integrate[F[x^2/(a + b*x)^2], x]

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fricas [A]  time = 0.40, size = 0, normalized size = 0.00 \[ {\rm integral}\left (F\left (\frac {x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right ), x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x^2/(b*x+a)^2),x, algorithm="fricas")

[Out]

integral(F(x^2/(b^2*x^2 + 2*a*b*x + a^2)), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F\left (\frac {x^{2}}{{\left (b x + a\right )}^{2}}\right )\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x^2/(b*x+a)^2),x, algorithm="giac")

[Out]

integrate(F(x^2/(b*x + a)^2), x)

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maple [A]  time = 0.02, size = 0, normalized size = 0.00 \[ \int F \left (\frac {x^{2}}{\left (b x +a \right )^{2}}\right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F(x^2/(b*x+a)^2),x)

[Out]

int(F(x^2/(b*x+a)^2),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F\left (\frac {x^{2}}{{\left (b x + a\right )}^{2}}\right )\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x^2/(b*x+a)^2),x, algorithm="maxima")

[Out]

integrate(F(x^2/(b*x + a)^2), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.07 \[ \int F\left (\frac {x^2}{{\left (a+b\,x\right )}^2}\right ) \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F(x^2/(a + b*x)^2),x)

[Out]

int(F(x^2/(a + b*x)^2), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F{\left (\frac {x^{2}}{\left (a + b x\right )^{2}} \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x**2/(b*x+a)**2),x)

[Out]

Integral(F(x**2/(a + b*x)**2), x)

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