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

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

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integral of sin(2x)*sec(x)

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

- 2 cos (x) + C

Solution steps

\int sin (2 x) sec (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

\int \frac{6 x ^{3} - 12 x ^{2} + 4}{x ^{2} - 2 x} d x

x \to 2 π lim (\frac{x - 2 π}{sin ( x )})

\frac{d}{d x} (tan (b x))

x cos (5 x)

(y + x + \frac{y ^{2}}{x}) d x - x d y = 0

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