I like integrals 4

Calculus Level 4

$\displaystyle\int _{ 0 }^{ 1 }{ \dfrac { \sinh { x } }{ { e }^{ x } } dx } =\frac { 1 }{ A{ e }^{ B } } +\frac { 1 }{ C }$

The equation above holds true for integer constants $A,B$ and $C$ . Find $A+B+C$ .

1 solution

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Apr 16, 2016

$\displaystyle\int_{0}^{1}\frac{\sinh{x}}{e^x} = \int_{0}^{1} \frac{1}{2}-\frac{1}{2e^2x} = \frac{1}{4e^2}+\frac{1}{4}$

$\bf Note:$

$\displaystyle\sinh{x}=\frac{e^x-e^{-x}}{2}$