Question

If int (eˣcos x)/(1+sin x)dx is equal to

• A. \(\dfrac{e^x\cos x}{1+\sin x}+C\)
• B. \(C-\dfrac{e^x\sin x}{1+\sin x}\)
• C. \(C-\dfrac{e^x}{1+\sin x}\)
• D. C-(eˣcos x)/(1+sin x)

Hint:

Often verify integrals by differentiating the given options.

Answer 1

The Correct Option is C

Differentiating -(eˣ)/(1+sin x) gives (eˣcos x)/(1+sin x). Hence the integral equals C-(eˣ)/(1+sin x).