What is the integral of (tan(x))/(sqrt(cos(x))) ?

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

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integral of (tan(x))/(sqrt(cos(x)))

\int \frac{tan ( x )}{cos ( x )} d x

2 sec (x) + C

Solution steps

\int \frac{tan ( x )}{cos ( x )} d x

Rewrite using trig identities

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

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 (x)

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

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 sec (x)

Add a constant to the solution

= 2 sec (x) + C

14 y^{^{''}} + y^{^{'}} + y = x^{2} - 2 x

\frac{\partial}{\partial y} (2 x y^{2})

\int_{0}^{8 π} x^{2} sin (2 x) d x

sin (tan (ln (x^{2} + 5)))

f (x) = - 15 x^{2} - 14 x + 8

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