Let I=∫exe4x+e2x+1dx,J=∫e−xe−4x+e−2x+1dx, Then, for an arbitrary constant C, the value of J-I equals

# Let $I=\int \frac{{e}^{x}}{{e}^{4x}+{e}^{2x}+1}dx,J=\int \frac{{e}^{-x}}{{e}^{-4x}+{e}^{-2x}+1}dx,$ Then, for an arbitrary constant $C,$ the value of J-I equals

1. A

$\frac{1}{2}\mathrm{log}\left(\frac{{e}^{4x}-{e}^{2x}+1}{{e}^{4x}+{e}^{2x}+1}\right)+C$

2. B

$\frac{1}{2}\mathrm{log}\left(\frac{{e}^{2x}+{e}^{x}\mid +1}{{e}^{2x}-{e}^{x}+1}\right)+C$

3. C

$\frac{1}{2}\mathrm{log}\left(\frac{{e}^{2x}-{e}^{x}+1}{{e}^{2x}+{e}^{x}+1}\right)+C$

4. D

$\frac{1}{2}\mathrm{log}\left(\frac{{e}^{4x}+{e}^{2x}+1}{{e}^{4x}-{e}^{2x}+1}\right)+C$

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

We have,

where $t={e}^{x}$

## Related content

 CBSE Syllabus for Class 6 World War 2 French Revolution Quit India Movement CBSE Class 12 Geography Paper Analysis 2024 (OUT) Decoding NEET UG 2024: Understanding Tie Breaking Criteria for Medical Aspirants NEET 2024 Exam Centers Out – Cities Expanded to 544 Nationwide! English Poems for Class 3 CBSE Class 12 Geography Question Paper 2024 PDF Download Science Project Ideas For Class 5

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)