What is the integral of (sec(z)tan(z))/(sqrt(sec(z))) ?

The integral of (sec(z)tan(z))/(sqrt(sec(z))) is 2sqrt(sec(z))+C

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integral of (sec(z)tan(z))/(sqrt(sec(z)))

\int \frac{sec ( z ) tan ( z )}{sec ( z )} d z

2 sec (z) + C

Solution steps

\int \frac{sec ( z ) tan ( z )}{sec ( z )} d z

Rewrite using trig identities

= \int \frac{sin ( z ) sec ( z )}{cos ( z )} d z

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

= \int tan (z) sec (z) d z

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 2 u^{\frac{1}{2}}

Substitute back

u = sec (z)

= 2 sec^{\frac{1}{2}} (z)

Apply radical rule:

= 2 sec (z)

Add a constant to the solution

= 2 sec (z) + C

(1 - 25 x^{2})^{2} arcsin (5 x)

\frac{64}{x ^{2} + 16}, at x = 3

\int_{2}^{3} (x^{2} - 4) d x

f (x) = \frac{6 x}{2 + x ^{2}}, (2, 2)

\int (3 x + 2) d x

What is the integral of (sec(z)tan(z))/(sqrt(sec(z))) ?
The integral of (sec(z)tan(z))/(sqrt(sec(z))) is 2sqrt(sec(z))+C