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The value of integral ∫x n-1 sin(x n )dx is: (where n is an integer)

The value of integral ∫xn-1sin(xn)dx is: (where n is an integer)

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Put x^n = t
Hence
n* x^(n-1) dx = dt
Now
x ^(n-1) dx = dt/n
Then your question becomes as
Sin t dt/n
On integrating
Answer is
(1/n)(-cos t) + C
Now put the value of t
Hence final anwer will be
(1/n) ( -cos (x^n)) + C

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