Question

∫e^sinx cosx dx is equal to ______.

Options

• e^{cos x} + c                                                                                                           

• e^{sin x} + C

• `sin^2 x/2 + c`

• `e^(sin^2x) + c`

Answer 1

∫e^sinx cosx dx is equal to e^{sin x} + C.

Explanation:

∫e^sinx cosx dx 

Let,

On differentiating w.r.t. x

⇒ `cos x = dt/dx`

⇒ `dx = dt/cos x`

Now,

`∫e^t cos x xx dt/cos x`

= ∫e^tdt

= e^t + c

= e^sinx + c

Option e^{sin x} + C is correct.