Question

If int (cos x-1)/(sin x+eˣ)dx is equal to

• A. (eˣcos x)/(1+sin x)+C
• B. C-(eˣsin x)/(1+sin x)
• C. C-(eˣ)/(1+sin x)
• D. C-(eˣcos x)/(1+sin x)

Hint:

In such integrals, try differentiating the given options to identify the integrand.

Answer 1

The Correct Option is C

By inspection, differentiating (eˣ)/(1+sin x) yields a numerator involving cos x-1 after simplification. Hence, int (cos x-1)/(sin x+eˣ)dx = C-(eˣ)/(1+sin x)