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can someone help me integrate the following?

integrate from pi/6 to pi/2
(x+16/(sinx^2))dx

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Sup bro
 
I dont know if u noe this already but 1/sin^2(x) = csc^2(x)
 
So,
 
 
 
If you use the indefinite intergral of everything,
 
you should get ((x^2)/2) - 16cot(x) + C ............. since integration of csc^2(x) is - cot(x) + C
 
but since we are doing definite,
 
you just use the normal process of doing definite integration.
 
i.e. substitute pi/2 on that and then subtract it by pi/6.
 
your exact final answer should be
 
(16√3) + (pi^2)/9

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