What is expand In(e^{2x}+1)^2 ?

The solution to expand In(e^{2x}+1)^2 is ne^{4x}I+2ne^{2x}I+nI

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expand In(e^{2x}+1)^2

expand

I n (e^{2 x} + 1)^{2}

n e^{4 x} I + 2 n e^{2 x} I + n I

Solution steps

I n (e^{2 x} + 1)^{2}

(e^{2 x} + 1)^{2} = e^{4 x} + 2 e^{2 x} + 1

= n I (e^{4 x} + 2 e^{2 x} + 1)

= n I (e^{4 x} + 2 e^{2 x} + 1)

Distribute parentheses

= I n e^{4 x} + I n \cdot 2 e^{2 x} + I n \cdot 1

= n e^{4 x} I + 2 n e^{2 x} I + 1 \cdot n I

Multiply:

1 \cdot n = n

= n e^{4 x} I + 2 n e^{2 x} I + n I

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What is expand In(e^{2x}+1)^2 ?
The solution to expand In(e^{2x}+1)^2 is ne^{4x}I+2ne^{2x}I+nI