What is the integral of sin(2θ) ?

The integral of sin(2θ) is -1/2 cos(2θ)+C

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integral of sin(2θ)

\int sin (2 θ) d θ

- \frac{1}{2} cos (2 θ) + C

Solution steps

\int sin (2 θ) d θ

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

= \int sin (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{2} (- cos (u))

Substitute back

u = 2 θ

= \frac{1}{2} (- cos (2 θ))

Simplify

= - \frac{1}{2} cos (2 θ)

Add a constant to the solution

= - \frac{1}{2} cos (2 θ) + C

f (s) = \frac{1}{s ( s - 3 )}

\frac{d}{d x} (arccot (2 x))

x \to 1 + lim (\frac{x + 10}{x + 3})

\frac{x ^{8} - 2 x ^{4} - 10 x}{x ^{4}}

6 ln (x), x ln (x)