Optimal. Leaf size=55 \[ \frac{\left (a+b \log \left (c x^n\right )\right ) \text{Chi}\left (d \left (a+b \log \left (c x^n\right )\right )\right )}{b n}-\frac{\sinh \left (d \left (a+b \log \left (c x^n\right )\right )\right )}{b d n} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0328463, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {6529} \[ \frac{\left (a+b \log \left (c x^n\right )\right ) \text{Chi}\left (d \left (a+b \log \left (c x^n\right )\right )\right )}{b n}-\frac{\sinh \left (d \left (a+b \log \left (c x^n\right )\right )\right )}{b d n} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 6529
Rubi steps
\begin{align*} \int \frac{\text{Chi}\left (d \left (a+b \log \left (c x^n\right )\right )\right )}{x} \, dx &=\frac{\operatorname{Subst}\left (\int \text{Chi}(d (a+b x)) \, dx,x,\log \left (c x^n\right )\right )}{n}\\ &=\frac{\operatorname{Subst}\left (\int \text{Chi}(x) \, dx,x,a d+b d \log \left (c x^n\right )\right )}{b d n}\\ &=\frac{\text{Chi}\left (a d+b d \log \left (c x^n\right )\right ) \left (a+b \log \left (c x^n\right )\right )}{b n}-\frac{\sinh \left (a d+b d \log \left (c x^n\right )\right )}{b d n}\\ \end{align*}
Mathematica [A] time = 0.0782421, size = 96, normalized size = 1.75 \[ \frac{a \text{Chi}\left (a d+b \log \left (c x^n\right ) d\right )}{b n}+\frac{\log \left (c x^n\right ) \text{Chi}\left (d \left (a+b \log \left (c x^n\right )\right )\right )}{n}-\frac{\sinh (a d) \cosh \left (b d \log \left (c x^n\right )\right )}{b d n}-\frac{\cosh (a d) \sinh \left (b d \log \left (c x^n\right )\right )}{b d n} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.079, size = 73, normalized size = 1.3 \begin{align*}{\frac{\ln \left ( c{x}^{n} \right ){\it Chi} \left ( ad+bd\ln \left ( c{x}^{n} \right ) \right ) }{n}}+{\frac{{\it Chi} \left ( ad+bd\ln \left ( c{x}^{n} \right ) \right ) a}{bn}}-{\frac{\sinh \left ( ad+bd\ln \left ( c{x}^{n} \right ) \right ) }{bdn}} \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 \frac{{\rm Chi}\left ({\left (b \log \left (c x^{n}\right ) + a\right )} d\right )}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\operatorname{Chi}\left (b d \log \left (c x^{n}\right ) + a d\right )}{x}, x\right ) \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 \frac{\operatorname{Chi}\left (a d + b d \log{\left (c x^{n} \right )}\right )}{x}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm Chi}\left ({\left (b \log \left (c x^{n}\right ) + a\right )} d\right )}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]