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Question
If `int x^5 cos (x^6)"d"x = "k" sin (x^6) + "C"`, find the value of k.
Solution
Given `int x^5 cos (x^6)"d"x = "k" sin (x^6) + "C"`
Put x6 = t
6x5 dx = dt
x5 dt = `"dt"/6` ...(i)
⇒ `int cos "t" "dt"/6` = k sin (x6) + C
⇒ `1/6` sin t + C = k sin (x6) + C
⇒ `1/6 sin (x^6) + "C" = "k" sin (x^6) + "C"`
On equating,
k = `1/6`
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