What is the integral from 0 to pi/3 of 1/(cos^2(2x)) ?

The integral from 0 to pi/3 of 1/(cos^2(2x)) is diverges

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integral from 0 to pi/3 of 1/(cos^2(2x))

\int_{0}^{\frac{π}{3}} \frac{1}{cos ^{2} ( 2 x )} d x

diverges

Solution steps

\int_{0}^{\frac{π}{3}} \frac{1}{cos ^{2} ( 2 x )} d x

Take the denominator(s) of

\frac{1}{cos ^{2} ( 2 x )}

and compare to zero:

x = \frac{π}{4}

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}{4}} \frac{1}{cos ^{2} ( 2 x )} d x + \int_{\frac{π}{4}}^{\frac{π}{3}} \frac{1}{cos ^{2} ( 2 x )} d x

\int_{0}^{\frac{π}{4}} \frac{1}{cos ^{2} ( 2 x )} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{- 1}^{3} (4 x^{3} + 7 x) d x

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\int_{2}^{0} c x d x

\int_{0}^{1} \frac{2}{x ^{3}} d x

What is the integral from 0 to pi/3 of 1/(cos^2(2x)) ?
The integral from 0 to pi/3 of 1/(cos^2(2x)) is diverges