3.19 \(\int \frac {x^2}{a+b \sec (c+d x^2)} \, dx\)

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {x^2}{a+b \sec \left (c+d x^2\right )},x\right ) \]

[Out]

Unintegrable(x^2/(a+b*sec(d*x^2+c)),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 = {} \[ \int \frac {x^2}{a+b \sec \left (c+d x^2\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[x^2/(a + b*Sec[c + d*x^2]),x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 1.17, size = 0, normalized size = 0.00 \[ \int \frac {x^2}{a+b \sec \left (c+d x^2\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.67, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x^{2}}{b \sec \left (d x^{2} + c\right ) + a}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(x^2/(b*sec(d*x^2 + c) + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^2/(b*sec(d*x^2 + c) + a), x)

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maple [A]  time = 0.83, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{a +b \sec \left (d \,x^{2}+c \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2/(a+b*sec(d*x^2+c)),x)

[Out]

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

[Out]

Timed out

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {x^2}{a+\frac {b}{\cos \left (d\,x^2+c\right )}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2/(a + b/cos(c + d*x^2)),x)

[Out]

int(x^2/(a + b/cos(c + d*x^2)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**2/(a+b*sec(d*x**2+c)),x)

[Out]

Integral(x**2/(a + b*sec(c + d*x**2)), x)

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