Question

If `int x^5 cos (x^6)dx = k sin (x^6) + C`, find the value of k.

Answer 1

Given `int x^5 cos (x^6)dx = k sin (x^6) + C`

Put x⁶ = t

6x⁵ dx = dt

`x^5 dt = (dt)/6`   ...(i)

⇒ `int cos t (dt)/6 = k sin (x^6) + C`

⇒ `1/6 sin t + C = k sin (x^6) + C`

⇒ `1/6 sin (x^6) + C = k sin (x^6) + C`

On equating,

k = `1/6`