What is the integral from 1 to 2 of (arccsc(x))/6 ?

The integral from 1 to 2 of (arccsc(x))/6 is 1/6 (ln(2+sqrt(3))-pi/6)

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integral from 1 to 2 of (arccsc(x))/6

\int_{1}^{2} \frac{arccsc ( x )}{6} d x

\frac{1}{6} (ln (2 + 3) - \frac{π}{6})

Decimal

0.13222 \dots

Solution steps

\int_{1}^{2} \frac{arccsc ( x )}{6} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int_{1}^{2} arccsc (x) d x

Apply Integration By Parts

: [x arccsc (x) - \int - \frac{x}{x ^{2} x ^{2} - 1} d x]_{1}^{2}

= \frac{1}{6} [x arccsc (x) - \int - \frac{x}{x ^{2} x ^{2} - 1} d x]_{1}^{2}

\int - \frac{x}{x ^{2} x ^{2} - 1} d x = - ln x + x^{2} - 1

= \frac{1}{6} [x arccsc (x) - (- ln x + x^{2} - 1)]_{1}^{2}

Simplify

= \frac{1}{6} [x arccsc (x) + ln x + x^{2} - 1]_{1}^{2}

Compute the boundaries:

ln (2 + 3) - \frac{π}{6}

= \frac{1}{6} (ln (2 + 3) - \frac{π}{6})

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What is the integral from 1 to 2 of (arccsc(x))/6 ?
The integral from 1 to 2 of (arccsc(x))/6 is 1/6 (ln(2+sqrt(3))-pi/6)