Optimal. Leaf size=50 \[ -b \text{CannotIntegrate}\left (\frac{\text{CosIntegral}(b x) \sin (b x)}{x},x\right )-\frac{\text{CosIntegral}(b x) \cos (b x)}{x}-b \text{Si}(2 b x)-\frac{\cos ^2(b x)}{x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0930662, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\cos (b x) \text{CosIntegral}(b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\cos (b x) \text{Ci}(b x)}{x^2} \, dx &=-\frac{\cos (b x) \text{Ci}(b x)}{x}+b \int \frac{\cos ^2(b x)}{b x^2} \, dx-b \int \frac{\text{Ci}(b x) \sin (b x)}{x} \, dx\\ &=-\frac{\cos (b x) \text{Ci}(b x)}{x}-b \int \frac{\text{Ci}(b x) \sin (b x)}{x} \, dx+\int \frac{\cos ^2(b x)}{x^2} \, dx\\ &=-\frac{\cos ^2(b x)}{x}-\frac{\cos (b x) \text{Ci}(b x)}{x}-b \int \frac{\text{Ci}(b x) \sin (b x)}{x} \, dx+(2 b) \int -\frac{\sin (2 b x)}{2 x} \, dx\\ &=-\frac{\cos ^2(b x)}{x}-\frac{\cos (b x) \text{Ci}(b x)}{x}-b \int \frac{\text{Ci}(b x) \sin (b x)}{x} \, dx-b \int \frac{\sin (2 b x)}{x} \, dx\\ &=-\frac{\cos ^2(b x)}{x}-\frac{\cos (b x) \text{Ci}(b x)}{x}-b \text{Si}(2 b x)-b \int \frac{\text{Ci}(b x) \sin (b x)}{x} \, dx\\ \end{align*}
Mathematica [A] time = 0.444453, size = 0, normalized size = 0. \[ \int \frac{\cos (b x) \text{CosIntegral}(b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.057, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\it Ci} \left ( bx \right ) \cos \left ( bx \right ) }{{x}^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm Ci}\left (b x\right ) \cos \left (b x\right )}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\cos \left (b x\right ) \operatorname{Ci}\left (b x\right )}{x^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cos{\left (b x \right )} \operatorname{Ci}{\left (b x \right )}}{x^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm Ci}\left (b x\right ) \cos \left (b x\right )}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]