What is the integral from 0 to 1 of tan^2(5x) ?

The integral from 0 to 1 of tan^2(5x) is diverges

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integral from 0 to 1 of tan^2(5x)

\int_{0}^{1} tan^{2} (5 x) d x

diverges

Solution steps

\int_{0}^{1} tan^{2} (5 x) d x

Take the denominator(s) of

tan^{2} (5 x)

and compare to zero:

x = \frac{π}{10}, x = \frac{3 π}{10}

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_{0}^{\frac{π}{10}} tan^{2} (5 x) d x + \int_{\frac{π}{10}}^{\frac{3 π}{10}} tan^{2} (5 x) d x + \int_{\frac{3 π}{10}}^{1} tan^{2} (5 x) d x

\int_{0}^{\frac{π}{10}} tan^{2} (5 x) d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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What is the integral from 0 to 1 of tan^2(5x) ?
The integral from 0 to 1 of tan^2(5x) is diverges