Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{x^3 \left (a+b \sin \left (c+d x^3\right )\right )},x\right ) \]
[Out]
________________________________________________________________________________________
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 = {} \[ \int \frac {1}{x^3 \left (a+b \sin \left (c+d x^3\right )\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {1}{x^3 \left (a+b \sin \left (c+d x^3\right )\right )} \, dx &=\int \frac {1}{x^3 \left (a+b \sin \left (c+d x^3\right )\right )} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.37, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^3 \left (a+b \sin \left (c+d x^3\right )\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.73, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{b x^{3} \sin \left (d x^{3} + c\right ) + a x^{3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b \sin \left (d x^{3} + c\right ) + a\right )} x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.08, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{3} \left (a +b \sin \left (d \,x^{3}+c \right )\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b \sin \left (d x^{3} + c\right ) + a\right )} x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{x^3\,\left (a+b\,\sin \left (d\,x^3+c\right )\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{3} \left (a + b \sin {\left (c + d x^{3} \right )}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________