Optimal. Leaf size=47 \[ \frac{4}{3} x^9 \sin \left (x^3\right )-8 x^3 \sin \left (x^3\right )-\frac{1}{3} x^{12} \cos \left (x^3\right )+4 x^6 \cos \left (x^3\right )-8 \cos \left (x^3\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0641899, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375, Rules used = {3379, 3296, 2638} \[ \frac{4}{3} x^9 \sin \left (x^3\right )-8 x^3 \sin \left (x^3\right )-\frac{1}{3} x^{12} \cos \left (x^3\right )+4 x^6 \cos \left (x^3\right )-8 \cos \left (x^3\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3379
Rule 3296
Rule 2638
Rubi steps
\begin{align*} \int x^{14} \sin \left (x^3\right ) \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int x^4 \sin (x) \, dx,x,x^3\right )\\ &=-\frac{1}{3} x^{12} \cos \left (x^3\right )+\frac{4}{3} \operatorname{Subst}\left (\int x^3 \cos (x) \, dx,x,x^3\right )\\ &=-\frac{1}{3} x^{12} \cos \left (x^3\right )+\frac{4}{3} x^9 \sin \left (x^3\right )-4 \operatorname{Subst}\left (\int x^2 \sin (x) \, dx,x,x^3\right )\\ &=4 x^6 \cos \left (x^3\right )-\frac{1}{3} x^{12} \cos \left (x^3\right )+\frac{4}{3} x^9 \sin \left (x^3\right )-8 \operatorname{Subst}\left (\int x \cos (x) \, dx,x,x^3\right )\\ &=4 x^6 \cos \left (x^3\right )-\frac{1}{3} x^{12} \cos \left (x^3\right )-8 x^3 \sin \left (x^3\right )+\frac{4}{3} x^9 \sin \left (x^3\right )+8 \operatorname{Subst}\left (\int \sin (x) \, dx,x,x^3\right )\\ &=-8 \cos \left (x^3\right )+4 x^6 \cos \left (x^3\right )-\frac{1}{3} x^{12} \cos \left (x^3\right )-8 x^3 \sin \left (x^3\right )+\frac{4}{3} x^9 \sin \left (x^3\right )\\ \end{align*}
Mathematica [A] time = 0.0315941, size = 35, normalized size = 0.74 \[ \frac{4}{3} x^3 \left (x^6-6\right ) \sin \left (x^3\right )-\frac{1}{3} \left (x^{12}-12 x^6+24\right ) \cos \left (x^3\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [C] time = 0.023, size = 64, normalized size = 1.4 \begin{align*} -{\frac{ \left ({x}^{12}+4\,i{x}^{9}-12\,{x}^{6}-24\,i{x}^{3}+24 \right ){{\rm e}^{i{x}^{3}}}}{6}}-{\frac{ \left ({x}^{12}-4\,i{x}^{9}-12\,{x}^{6}+24\,i{x}^{3}+24 \right ){{\rm e}^{-i{x}^{3}}}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.963759, size = 43, normalized size = 0.91 \begin{align*} -\frac{1}{3} \,{\left (x^{12} - 12 \, x^{6} + 24\right )} \cos \left (x^{3}\right ) + \frac{4}{3} \,{\left (x^{9} - 6 \, x^{3}\right )} \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.06486, size = 88, normalized size = 1.87 \begin{align*} -\frac{1}{3} \,{\left (x^{12} - 12 \, x^{6} + 24\right )} \cos \left (x^{3}\right ) + \frac{4}{3} \,{\left (x^{9} - 6 \, x^{3}\right )} \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 123.675, size = 48, normalized size = 1.02 \begin{align*} - \frac{x^{12} \cos{\left (x^{3} \right )}}{3} + \frac{4 x^{9} \sin{\left (x^{3} \right )}}{3} + 4 x^{6} \cos{\left (x^{3} \right )} - 8 x^{3} \sin{\left (x^{3} \right )} - 8 \cos{\left (x^{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.08185, size = 43, normalized size = 0.91 \begin{align*} -\frac{1}{3} \,{\left (x^{12} - 12 \, x^{6} + 24\right )} \cos \left (x^{3}\right ) + \frac{4}{3} \,{\left (x^{9} - 6 \, x^{3}\right )} \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]