Optimal. Leaf size=29 \[ -\frac{\text{Chi}(3 x)}{10}-\frac{\text{Chi}(7 x)}{10}+\frac{1}{5} \text{Chi}(2 x) \cosh (5 x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0563802, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 4, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.444, Rules used = {6547, 12, 5471, 3301} \[ -\frac{\text{Chi}(3 x)}{10}-\frac{\text{Chi}(7 x)}{10}+\frac{1}{5} \text{Chi}(2 x) \cosh (5 x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 6547
Rule 12
Rule 5471
Rule 3301
Rubi steps
\begin{align*} \int \text{Chi}(2 x) \sinh (5 x) \, dx &=\frac{1}{5} \cosh (5 x) \text{Chi}(2 x)-\frac{2}{5} \int \frac{\cosh (2 x) \cosh (5 x)}{2 x} \, dx\\ &=\frac{1}{5} \cosh (5 x) \text{Chi}(2 x)-\frac{1}{5} \int \frac{\cosh (2 x) \cosh (5 x)}{x} \, dx\\ &=\frac{1}{5} \cosh (5 x) \text{Chi}(2 x)-\frac{1}{5} \int \left (\frac{\cosh (3 x)}{2 x}+\frac{\cosh (7 x)}{2 x}\right ) \, dx\\ &=\frac{1}{5} \cosh (5 x) \text{Chi}(2 x)-\frac{1}{10} \int \frac{\cosh (3 x)}{x} \, dx-\frac{1}{10} \int \frac{\cosh (7 x)}{x} \, dx\\ &=\frac{1}{5} \cosh (5 x) \text{Chi}(2 x)-\frac{\text{Chi}(3 x)}{10}-\frac{\text{Chi}(7 x)}{10}\\ \end{align*}
Mathematica [A] time = 0.0265139, size = 27, normalized size = 0.93 \[ \frac{1}{10} (-\text{Chi}(3 x)-\text{Chi}(7 x)+2 \text{Chi}(2 x) \cosh (5 x)) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.128, size = 24, normalized size = 0.8 \begin{align*} -{\frac{{\it Chi} \left ( 3\,x \right ) }{10}}-{\frac{{\it Chi} \left ( 7\,x \right ) }{10}}+{\frac{{\it Chi} \left ( 2\,x \right ) \cosh \left ( 5\,x \right ) }{5}} \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{\rm Chi}\left (2 \, x\right ) \sinh \left (5 \, x\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \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 \sinh{\left (5 x \right )} \operatorname{Chi}\left (2 x\right )\, 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{\rm Chi}\left (2 \, x\right ) \sinh \left (5 \, x\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]