What is the integral of sec(x)sin(2x) ?

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

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integral of sec(x)sin(2x)

\int sec (x) sin (2 x) d x

- 2 cos (x) + C

Solution steps

\int sec (x) sin (2 x) d x

Rewrite using trig identities

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

Express with sin, cos

= 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

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