Question icon
Grade 12Integral Calculus

integrate the following integral
∫ 1 + cos x / 1 – cos x dx

Profile image of taniska
11 Years agoGrade 12
Answers icon

1 Answer

Profile image of Jitender Singh
11 Years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{1+cosx}{1-cosx}dx
I = \int \frac{2cos^{2}\frac{x}{2}}{2sin^{2}\frac{x}{2}}dx
I = \int cot^{2}\frac{x}{2}dx
I = \int (cosec^{2}\frac{x}{2}-1)dx
I = \int cosec^{2}\frac{x}{2}dx-\int dx
I = -2cot\frac{x}{2}-\int dx
I = -2cot\frac{x}{2}-x+c