Optimal. Leaf size=29 \[ -\frac{1}{10} \text{CosIntegral}(3 x)+\frac{1}{10} \text{CosIntegral}(7 x)+\frac{1}{5} \text{Si}(2 x) \sin (5 x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0556862, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 4, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.444, Rules used = {6517, 12, 4428, 3302} \[ -\frac{1}{10} \text{CosIntegral}(3 x)+\frac{1}{10} \text{CosIntegral}(7 x)+\frac{1}{5} \text{Si}(2 x) \sin (5 x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 6517
Rule 12
Rule 4428
Rule 3302
Rubi steps
\begin{align*} \int \cos (5 x) \text{Si}(2 x) \, dx &=\frac{1}{5} \sin (5 x) \text{Si}(2 x)-\frac{2}{5} \int \frac{\sin (2 x) \sin (5 x)}{2 x} \, dx\\ &=\frac{1}{5} \sin (5 x) \text{Si}(2 x)-\frac{1}{5} \int \frac{\sin (2 x) \sin (5 x)}{x} \, dx\\ &=\frac{1}{5} \sin (5 x) \text{Si}(2 x)-\frac{1}{5} \int \left (\frac{\cos (3 x)}{2 x}-\frac{\cos (7 x)}{2 x}\right ) \, dx\\ &=\frac{1}{5} \sin (5 x) \text{Si}(2 x)-\frac{1}{10} \int \frac{\cos (3 x)}{x} \, dx+\frac{1}{10} \int \frac{\cos (7 x)}{x} \, dx\\ &=-\frac{\text{Ci}(3 x)}{10}+\frac{\text{Ci}(7 x)}{10}+\frac{1}{5} \sin (5 x) \text{Si}(2 x)\\ \end{align*}
Mathematica [A] time = 0.0258747, size = 25, normalized size = 0.86 \[ \frac{1}{10} (-\text{CosIntegral}(3 x)+\text{CosIntegral}(7 x)+2 \text{Si}(2 x) \sin (5 x)) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.131, size = 24, normalized size = 0.8 \begin{align*} -{\frac{{\it Ci} \left ( 3\,x \right ) }{10}}+{\frac{{\it Ci} \left ( 7\,x \right ) }{10}}+{\frac{{\it Si} \left ( 2\,x \right ) \sin \left ( 5\,x \right ) }{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\rm Si}\left (2 \, x\right ) \cos \left (5 \, x\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \cos{\left (5 x \right )} \operatorname{Si}{\left (2 x \right )}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.18164, size = 31, normalized size = 1.07 \begin{align*} \frac{1}{5} \, \sin \left (5 \, x\right ) \operatorname{Si}\left (2 \, x\right ) + \frac{1}{10} \, \operatorname{Ci}\left (7 \, x\right ) - \frac{1}{10} \, \operatorname{Ci}\left (3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]