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

The integral from pi/2 to pi of sec^3(x) is diverges

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integral from pi/2 to pi of sec^3(x)

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

diverges

Solution steps

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

Apply Integral Reduction

= [\frac{sec ^{2} ( x ) sin ( x )}{2}]_{\frac{π}{2}}^{π} + \frac{1}{2} \cdot \int_{\frac{π}{2}}^{π} sec (x) d x

\int_{\frac{π}{2}}^{π} sec (x) d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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