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) 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

y = x^{10 c o s (x)}

y = 4 tan (x), at x = \frac{π}{6}

\int_{1}^{3} (x^{2} + 1)^{3} x d x

\int_{2}^{4} \frac{1}{( x - 4 ) ( x - 1 )} d x

\int_{9}^{16} \frac{1}{2 - x} d x

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