What is the integral from pi/4 to pi/2 of cot^3(x) ?

The integral from pi/4 to pi/2 of cot^3(x) is 1/2-1/2 ln(2)

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integral from pi/4 to pi/2 of cot^3(x)

\int_{\frac{π}{4}}^{\frac{π}{2}} cot^{3} (x) d x

\frac{1}{2} - \frac{1}{2} ln (2)

Decimal

0.15342 \dots

Solution steps

\int_{\frac{π}{4}}^{\frac{π}{2}} cot^{3} (x) d x

Apply Integral Reduction

= - [\frac{cot ^{2} ( x )}{2}]_{\frac{π}{4}}^{\frac{π}{2}} - \int_{\frac{π}{4}}^{\frac{π}{2}} cot (x) d x

\int_{\frac{π}{4}}^{\frac{π}{2}} cot (x) d x = \frac{1}{2} ln (2)

= - [\frac{cot ^{2} ( x )}{2}]_{\frac{π}{4}}^{\frac{π}{2}} - \frac{1}{2} ln (2)

Compute the boundaries:

- \frac{1}{2}

= - (- \frac{1}{2}) - \frac{1}{2} ln (2)

Simplify

= \frac{1}{2} - \frac{1}{2} ln (2)

What is the integral from pi/4 to pi/2 of cot^3(x) ?
The integral from pi/4 to pi/2 of cot^3(x) is 1/2-1/2 ln(2)