Optimal. Leaf size=37 \[ \text {Int}\left (\frac {\left (a+b x^2\right )^{3/2} \sqrt {c+d x^2}}{\left (e+f x^2\right )^{3/2}},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.06, 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 = {} \[ \int \frac {\left (a+b x^2\right )^{3/2} \sqrt {c+d x^2}}{\left (e+f x^2\right )^{3/2}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^{3/2} \sqrt {c+d x^2}}{\left (e+f x^2\right )^{3/2}} \, dx &=\int \frac {\left (a+b x^2\right )^{3/2} \sqrt {c+d x^2}}{\left (e+f x^2\right )^{3/2}} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.91, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+b x^2\right )^{3/2} \sqrt {c+d x^2}}{\left (e+f x^2\right )^{3/2}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [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]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b x^{2} + a\right )}^{\frac {3}{2}} \sqrt {d x^{2} + c}}{{\left (f x^{2} + e\right )}^{\frac {3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.08, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \,x^{2}+a \right )^{\frac {3}{2}} \sqrt {d \,x^{2}+c}}{\left (f \,x^{2}+e \right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b x^{2} + a\right )}^{\frac {3}{2}} \sqrt {d x^{2} + c}}{{\left (f x^{2} + e\right )}^{\frac {3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {{\left (b\,x^2+a\right )}^{3/2}\,\sqrt {d\,x^2+c}}{{\left (f\,x^2+e\right )}^{3/2}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (a + b x^{2}\right )^{\frac {3}{2}} \sqrt {c + d x^{2}}}{\left (e + f x^{2}\right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________