What is the integral from 0 to pi/4 of xsec(x)tan(x) ?

The integral from 0 to pi/4 of xsec(x)tan(x) is pi/(2sqrt(2))-ln(1+sqrt(2))

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integral from 0 to pi/4 of xsec(x)tan(x)

\int_{0}^{\frac{π}{4}} x sec (x) tan (x) d x

\frac{π}{2 2} - ln (1 + 2)

Decimal

0.22934 \dots

Solution steps

\int_{0}^{\frac{π}{4}} x sec (x) tan (x) d x

Apply Integration By Parts

: [x sec (x) - \int sec (x) d x]_{0}^{\frac{π}{4}}

= [x sec (x) - \int sec (x) d x]_{0}^{\frac{π}{4}}

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= [x sec (x) - ln ∣ tan (x) + sec (x) ∣]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{π}{2 2} - ln (1 + 2)

= \frac{π}{2 2} - ln (1 + 2)

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\int_{0}^{π} (sin (x))^{5} d x

What is the integral from 0 to pi/4 of xsec(x)tan(x) ?
The integral from 0 to pi/4 of xsec(x)tan(x) is pi/(2sqrt(2))-ln(1+sqrt(2))