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integrate the following integral ∫ (e^x +1/e^x)^2 dx

 
integrate the following integral
∫ (e^x +1/e^x)^2 dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int (\frac{e^x+1}{e^x})^2dx
I = \int (1+e^{-x})^2dx
I = \int (1+e^{-2x}+2e^{-x})dx
I = \int dx+\int e^{-2x}dx+2\int e^{-x}dx
I = x+\int e^{-2x}dx+2\int e^{-x}dx
I = x-\frac{e^{-2x}}{2}+2\int e^{-x}dx
I = x-\frac{e^{-2x}}{2}-2e^{-x}+c

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