Optimal. Leaf size=33 \[ \frac {\text {Chi}(a+b x) \sinh (a+b x)}{b}-\frac {\text {Shi}(2 a+2 b x)}{2 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.06, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.308, Rules used = {6541, 5448, 12, 3298} \[ \frac {\text {Chi}(a+b x) \sinh (a+b x)}{b}-\frac {\text {Shi}(2 a+2 b x)}{2 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 3298
Rule 5448
Rule 6541
Rubi steps
\begin {align*} \int \cosh (a+b x) \text {Chi}(a+b x) \, dx &=\frac {\text {Chi}(a+b x) \sinh (a+b x)}{b}-\int \frac {\cosh (a+b x) \sinh (a+b x)}{a+b x} \, dx\\ &=\frac {\text {Chi}(a+b x) \sinh (a+b x)}{b}-\int \frac {\sinh (2 a+2 b x)}{2 (a+b x)} \, dx\\ &=\frac {\text {Chi}(a+b x) \sinh (a+b x)}{b}-\frac {1}{2} \int \frac {\sinh (2 a+2 b x)}{a+b x} \, dx\\ &=\frac {\text {Chi}(a+b x) \sinh (a+b x)}{b}-\frac {\text {Shi}(2 a+2 b x)}{2 b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 32, normalized size = 0.97 \[ \frac {\text {Chi}(a+b x) \sinh (a+b x)}{b}-\frac {\text {Shi}(2 (a+b x))}{2 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [F] time = 0.59, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\cosh \left (b x + a\right ) \operatorname {Chi}\left (b x + a\right ), x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm Chi}\left (b x + a\right ) \cosh \left (b x + a\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 30, normalized size = 0.91 \[ \frac {\Chi \left (b x +a \right ) \sinh \left (b x +a \right )-\frac {\Shi \left (2 b x +2 a \right )}{2}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm Chi}\left (b x + a\right ) \cosh \left (b x + a\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.03 \[ \int \mathrm {coshint}\left (a+b\,x\right )\,\mathrm {cosh}\left (a+b\,x\right ) \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \cosh {\left (a + b x \right )} \operatorname {Chi}\left (a + b x\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________