Optimal. Leaf size=29 \[ -\frac {\text {Chi}(3 x)}{10}-\frac {\text {Chi}(7 x)}{10}+\frac {1}{5} \text {Chi}(2 x) \cosh (5 x) \]
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Rubi [A] time = 0.06, antiderivative size = 29, normalized size of antiderivative = 1.00, 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.
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Rule 12
Rule 3301
Rule 5471
Rule 6547
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*}
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Mathematica [A] time = 0.03, 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.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm Chi}\left (2 \, x\right ) \sinh \left (5 \, x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 24, normalized size = 0.83 \[ -\frac {\Chi \left (3 x \right )}{10}-\frac {\Chi \left (7 x \right )}{10}+\frac {\Chi \left (2 x \right ) \cosh \left (5 x \right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm Chi}\left (2 \, x\right ) \sinh \left (5 \, x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \[ \int \mathrm {coshint}\left (2\,x\right )\,\mathrm {sinh}\left (5\,x\right ) \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \sinh {\left (5 x \right )} \operatorname {Chi}\left (2 x\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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