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

The integral from 0 to pi/3 of xsec^2(x) is pi/(sqrt(3))-ln(2)

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

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

\frac{π}{3} - ln (2)

Solution steps

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

Apply Integration By Parts

: [x tan (x) - \int tan (x) d x]_{0}^{\frac{π}{3}}

= [x tan (x) - \int tan (x) d x]_{0}^{\frac{π}{3}}

\int tan (x) d x = - ln ∣ cos (x) ∣

= [x tan (x) - (- ln ∣ cos (x) ∣)]_{0}^{\frac{π}{3}}

Simplify

= [x tan (x) + ln ∣ cos (x) ∣]_{0}^{\frac{π}{3}}

Compute the boundaries:

\frac{π}{3} - ln (2)

= \frac{π}{3} - ln (2)

2 x, x^{2}

\int \frac{2 x + y + z}{( x + y ) ( x + z )} d x

8 x^{2} - 7 x, at 9

y^{3} - (6 x + 8) + 3 x y^{2} y^{^{'}} = 0

4 y^{^{''}} + 4 y^{^{'}} + 1 y = 0, y (2) = - 6, y^{^{'}} (2) = 4

What is the integral from 0 to pi/3 of xsec^2(x) ?
The integral from 0 to pi/3 of xsec^2(x) is pi/(sqrt(3))-ln(2)