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

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

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

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

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 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = sec (x)

= 1 \cdot sec (x)

Simplify

= sec (x)

Add a constant to the solution

= sec (x) + C

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