Optimal. Leaf size=27 \[ b \text{Unintegrable}\left (\frac{\sin \left (c+d (f+g x)^n\right )}{x^2},x\right )-\frac{a}{x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0184941, 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 = {} \[ \int \frac{a+b \sin \left (c+d (f+g x)^n\right )}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{a+b \sin \left (c+d (f+g x)^n\right )}{x^2} \, dx &=\int \left (\frac{a}{x^2}+\frac{b \sin \left (c+d (f+g x)^n\right )}{x^2}\right ) \, dx\\ &=-\frac{a}{x}+b \int \frac{\sin \left (c+d (f+g x)^n\right )}{x^2} \, dx\\ \end{align*}
Mathematica [A] time = 2.67523, size = 0, normalized size = 0. \[ \int \frac{a+b \sin \left (c+d (f+g x)^n\right )}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.118, size = 0, normalized size = 0. \begin{align*} \int{\frac{a+b\sin \left ( c+d \left ( gx+f \right ) ^{n} \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*} b \int \frac{\sin \left ({\left (g x + f\right )}^{n} d + c\right )}{x^{2}}\,{d x} - \frac{a}{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{b \sin \left ({\left (g x + f\right )}^{n} d + c\right ) + a}{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{a + b \sin{\left (c + d \left (f + g x\right )^{n} \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{b \sin \left ({\left (g x + f\right )}^{n} d + c\right ) + a}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]