int frac{1+2 e^{-x}}{1-2 e^{-x}} d x= | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $I = \int \frac{1+2 e^{-x}}{1-2 e^{-x}} d x$. We can rewrite the numerator as $(1-2e^{-x}) + 4e^{-x}$. So,$I = \int \frac{(1-2e^{-x}) + 4e^{-x

Vedclass · Accepted Answer

$x+2\log \left|1-2 e^{-x}\right|+c$

Vedclass · Answer

(C) Let $I = \int \frac{1+2 e^{-x}}{1-2 e^{-x}} d x$. We can rewrite the numerator as $(1-2e^{-x}) + 4e^{-x}$. So,$I = \int \frac{(1-2e^{-x}) + 4e^{-x}}{1-2e^{-x}} d x$. $I = \int \left( 1 + \frac{4e^{-x}}{1-2e^{-x}} \right) d x$. $I = \int 1 d x + 2 \int \frac{2e^{-x}}{1-2e^{-x}} d x$. Let $u = 1-2e^{-x}$,then $du = 2e^{-x} d x$. $I = x + 2 \int \frac{1}{u} du = x + 2 \ln|u| + c$. Substituting back $u$,we get $I = x + 2 \ln|1-2e^{-x}| + c$.

$\int \frac{1+2 e^{-x}}{1-2 e^{-x}} d x=$

Similar Questions

$\int \frac{\sec x \, dx}{\sqrt{\cos 2x}} = $

Integrate the function: $\frac{\cos x}{\sqrt{4-\sin ^{2} x}}$

Integrate the function $\sec ^{2}(7-4 x)$.

If $f(x) = \int \frac{5x^8 + 7x^6}{(x^2 + 1 + 2x^7)^2} dx, x \geq 0$ and $f(0) = 0$,then the value of $f(1)$ is

$\int \frac{\sec^2 x \, dx}{\sqrt{\tan^2 x + 4}} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module