What is the integral from 0 to pi/3 of tan(x)+sec(x) ?

The integral from 0 to pi/3 of tan(x)+sec(x) is ln(2)+ln(2+sqrt(3))

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integral from 0 to pi/3 of tan(x)+sec(x)

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

ln (2) + ln (2 + 3)

Decimal

2.01010 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{\frac{π}{3}} tan (x) d x + \int_{0}^{\frac{π}{3}} sec (x) d x

\int_{0}^{\frac{π}{3}} tan (x) d x = ln (2)

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

= ln (2) + ln (2 + 3)

What is the integral from 0 to pi/3 of tan(x)+sec(x) ?
The integral from 0 to pi/3 of tan(x)+sec(x) is ln(2)+ln(2+sqrt(3))