Integrand size = 9, antiderivative size = 29 \[ \int \sin (5 x) \text {Si}(2 x) \, dx=-\frac {1}{5} \cos (5 x) \text {Si}(2 x)-\frac {\text {Si}(3 x)}{10}+\frac {\text {Si}(7 x)}{10} \]
[Out]
Time = 0.04 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.444, Rules used = {6646, 12, 4515, 3380} \[ \int \sin (5 x) \text {Si}(2 x) \, dx=-\frac {\text {Si}(3 x)}{10}+\frac {\text {Si}(7 x)}{10}-\frac {1}{5} \text {Si}(2 x) \cos (5 x) \]
[In]
[Out]
Rule 12
Rule 3380
Rule 4515
Rule 6646
Rubi steps \begin{align*} \text {integral}& = -\frac {1}{5} \cos (5 x) \text {Si}(2 x)+\frac {2}{5} \int \frac {\cos (5 x) \sin (2 x)}{2 x} \, dx \\ & = -\frac {1}{5} \cos (5 x) \text {Si}(2 x)+\frac {1}{5} \int \frac {\cos (5 x) \sin (2 x)}{x} \, dx \\ & = -\frac {1}{5} \cos (5 x) \text {Si}(2 x)+\frac {1}{5} \int \left (-\frac {\sin (3 x)}{2 x}+\frac {\sin (7 x)}{2 x}\right ) \, dx \\ & = -\frac {1}{5} \cos (5 x) \text {Si}(2 x)-\frac {1}{10} \int \frac {\sin (3 x)}{x} \, dx+\frac {1}{10} \int \frac {\sin (7 x)}{x} \, dx \\ & = -\frac {1}{5} \cos (5 x) \text {Si}(2 x)-\frac {\text {Si}(3 x)}{10}+\frac {\text {Si}(7 x)}{10} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.86 \[ \int \sin (5 x) \text {Si}(2 x) \, dx=\frac {1}{10} (-2 \cos (5 x) \text {Si}(2 x)-\text {Si}(3 x)+\text {Si}(7 x)) \]
[In]
[Out]
Time = 1.22 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.83
method | result | size |
default | \(-\frac {\cos \left (5 x \right ) \operatorname {Si}\left (2 x \right )}{5}-\frac {\operatorname {Si}\left (3 x \right )}{10}+\frac {\operatorname {Si}\left (7 x \right )}{10}\) | \(24\) |
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.41 \[ \int \sin (5 x) \text {Si}(2 x) \, dx=-\frac {16}{5} \, \cos \left (x\right )^{5} \operatorname {Si}\left (2 \, x\right ) + 4 \, \cos \left (x\right )^{3} \operatorname {Si}\left (2 \, x\right ) - \cos \left (x\right ) \operatorname {Si}\left (2 \, x\right ) + \frac {1}{10} \, \operatorname {Si}\left (7 \, x\right ) - \frac {1}{10} \, \operatorname {Si}\left (3 \, x\right ) \]
[In]
[Out]
\[ \int \sin (5 x) \text {Si}(2 x) \, dx=\int \sin {\left (5 x \right )} \operatorname {Si}{\left (2 x \right )}\, dx \]
[In]
[Out]
\[ \int \sin (5 x) \text {Si}(2 x) \, dx=\int { \sin \left (5 \, x\right ) \operatorname {Si}\left (2 \, x\right ) \,d x } \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.79 \[ \int \sin (5 x) \text {Si}(2 x) \, dx=-\frac {1}{5} \, \cos \left (5 \, x\right ) \operatorname {Si}\left (2 \, x\right ) + \frac {1}{10} \, \operatorname {Si}\left (7 \, x\right ) - \frac {1}{10} \, \operatorname {Si}\left (3 \, x\right ) \]
[In]
[Out]
Timed out. \[ \int \sin (5 x) \text {Si}(2 x) \, dx=\int \mathrm {sinint}\left (2\,x\right )\,\sin \left (5\,x\right ) \,d x \]
[In]
[Out]