What is expand e^xtanh(x)\times (2csch(2x)+1) ?

The solution to expand e^xtanh(x)\times (2csch(2x)+1) is 2e^xtanh(x)csch(2x)+e^xtanh(x)

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expand e^xtanh(x)\times (2csch(2x)+1)

expand

e^{x} tanh (x) \cdot (2 csch (2 x) + 1)

2 e^{x} tanh (x) csch (2 x) + e^{x} tanh (x)

Solution steps

e^{x} tanh (x) (2 csch (2 x) + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{x} tanh (x), b = 2 csch (2 x), c = 1

= e^{x} tanh (x) \cdot 2 csch (2 x) + e^{x} tanh (x) \cdot 1

= 2 e^{x} tanh (x) csch (2 x) + 1 \cdot e^{x} tanh (x)

Multiply:

1 \cdot e^{x} = e^{x}

= 2 e^{x} tanh (x) csch (2 x) + e^{x} tanh (x)

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What is expand e^xtanh(x)\times (2csch(2x)+1) ?
The solution to expand e^xtanh(x)\times (2csch(2x)+1) is 2e^xtanh(x)csch(2x)+e^xtanh(x)