Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{\left (a+b \sin \left (c+d (f+g x)^n\right )\right )^2}{x},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.024356, 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 = {} \[ \int \frac{\left (a+b \sin \left (c+d (f+g x)^n\right )\right )^2}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\left (a+b \sin \left (c+d (f+g x)^n\right )\right )^2}{x} \, dx &=\int \frac{\left (a+b \sin \left (c+d (f+g x)^n\right )\right )^2}{x} \, dx\\ \end{align*}
Mathematica [A] time = 3.65128, size = 0, normalized size = 0. \[ \int \frac{\left (a+b \sin \left (c+d (f+g x)^n\right )\right )^2}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.335, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( a+b\sin \left ( c+d \left ( gx+f \right ) ^{n} \right ) \right ) ^{2}}{x}}\, 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*} -\frac{1}{2} \, b^{2} \int \frac{\cos \left (2 \,{\left (g x + f\right )}^{n} d + 2 \, c\right )}{x}\,{d x} + 2 \, a b \int \frac{\sin \left ({\left (g x + f\right )}^{n} d + c\right )}{x}\,{d x} + a^{2} \log \left (x\right ) + \frac{1}{2} \, b^{2} \log \left (x\right ) \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{b^{2} \cos \left ({\left (g x + f\right )}^{n} d + c\right )^{2} - 2 \, a b \sin \left ({\left (g x + f\right )}^{n} d + c\right ) - a^{2} - b^{2}}{x}, 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{\left (a + b \sin{\left (c + d \left (f + g x\right )^{n} \right )}\right )^{2}}{x}\, 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{{\left (b \sin \left ({\left (g x + f\right )}^{n} d + c\right ) + a\right )}^{2}}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]