Emily-Jane Bray

2021-09-16

Evaluate the integral.

$\int \frac{{2}^{x}}{{2}^{x}+1}dx$

jlo2niT

Skilled2021-09-17Added 96 answers

Step 1

Consider the integrals:

$\int \frac{{2}^{x}}{{2}^{x}+1}dx$

To solve the given integrals,

Let,

${2}^{x}+1=t$

Differentiating with respect to "t"

${2}^{x}\mathrm{ln}2dx+0=dt$

$2}^{x}dx=\frac{dt}{\mathrm{ln}2$

Step 2

Substitute all value in equation given integrals,

$\int \frac{{2}^{x}}{{2}^{x}+1}dx=\int \frac{1}{t}\frac{dt}{\mathrm{ln}2}$

$=\frac{1}{\mathrm{ln}2}\int \frac{1}{t}dt$

$=\frac{1}{\mathrm{ln}2}\cdot \mathrm{ln}\left|t\right|+C$

$=\frac{1}{\mathrm{ln}2}\cdot \mathrm{ln}|{2}^{x}+1|+C$

Consider the integrals:

To solve the given integrals,

Let,

Differentiating with respect to "t"

Step 2

Substitute all value in equation given integrals,

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