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Grade 12Integral Calculus

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

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 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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