What is the integral from 2 to 3 of csc^2(3x-1) ?

The integral from 2 to 3 of csc^2(3x-1) is diverges

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integral from 2 to 3 of csc^2(3x-1)

\int_{2}^{3} csc^{2} (3 x - 1) d x

diverges

Solution steps

\int_{2}^{3} csc^{2} (3 x - 1) d x

Take the denominator(s) of

csc^{2} (3 x - 1)

and compare to zero:

x = \frac{2 π + 1}{3}

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{2}^{\frac{2 π + 1}{3}} csc^{2} (3 x - 1) d x + \int_{\frac{2 π + 1}{3}}^{3} csc^{2} (3 x - 1) d x

\int_{2}^{\frac{2 π + 1}{3}} csc^{2} (3 x - 1) d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{1}^{2} \frac{x ^{2} - 1}{x ^{4}} d x

\int_{0}^{2} \frac{2}{x - 1} d x

\int_{0}^{4} (2 x + 1)^{\frac{1}{2}} d x

\int_{\frac{π}{2}}^{\frac{3 π}{2}} 3 cos (x) d x

What is the integral from 2 to 3 of csc^2(3x-1) ?
The integral from 2 to 3 of csc^2(3x-1) is diverges