What is the integral of ((sin(2x)))/(cos(x)) ?

The integral of ((sin(2x)))/(cos(x)) is -2cos(x)+C

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integral of ((sin(2x)))/(cos(x))

\int \frac{( sin ( 2 x ) )}{cos ( x )} d x

- 2 cos (x) + C

Solution steps

\int \frac{sin ( 2 x )}{cos ( x )} d x

Rewrite using trig identities

= \int 2 sin (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= 2 (- cos (x))

Simplify

= - 2 cos (x)

Add a constant to the solution

= - 2 cos (x) + C

What is the integral of ((sin(2x)))/(cos(x)) ?
The integral of ((sin(2x)))/(cos(x)) is -2cos(x)+C