Question

`intcos^3x  dx` = ______ 

विकल्प

• `1/4 sinx + 1/12 sin3x  + c`

• `3/4sinx + 1/3sin 3x + c`

• `3/4sinx + 1/12 sin3x + c`

• `1/3sinx + 1/6sin3x + c`

Answer 1

`intcos^3x  dx` = `underline(3/4sinx + 1/12 sin3x + c)`

Explanation:

`intcos^3x  dx`

= `int(3cosx + cos3x)/4 dx` .....[∵ cos 3x = 4cos³x - 3cosx]

= `3/4intcosx  dx + 1/4intcos3x  dx`

= `3/4sinx + 1/4((sin3x)/3) + c`

= `(3sinx)/4 + (sin3x)/12 + c`

= `3/4sinx + 1/12sin3x + c`