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Integral Calculus> ∫ dx/e x +4e -x = f (x) + c then f (x) is...

question mark

∫ dx/e^x +4e^-x =f (x) + c then f (x) is equal to
options
1)2 tan^-1 (2e^x)

1/2 tan-1 (ex/2)

2tan^-1 e^x/2

1/2 tan^-1 (2e^2x)

Aditya Kartikeya , 11 Years ago

Grade 10

1 Answers

Jitender Singh

Ans:
Hello Student,
Please find answer to your question below

$\int \frac{dx}{e^{x} + 4e^{-x}} = f(x) + c$
$I = \int \frac{dx}{e^{x} + 4e^{-x}}$
$I = \int \frac{e^{x}}{e^{2x}+4}dx$
$I = \int \frac{e^{x}}{(e^{x})^{2}+(2)^{2}}dx$
$e^{x} = t$
$e^{x}dx = dt$
$I = \int \frac{1}{t^{2}+(2)^{2}}dt$
$I = \frac{1}{2}tan^{-1}(\frac{t}{2}) + c$
$I = \frac{1}{2}tan^{-1}(\frac{e^{x}}{2}) + c$

Last Activity: 11 Years ago

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