What is the integral of cos(2θ) ?

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

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integral of cos(2θ)

\int cos (2 θ) d θ

\frac{1}{2} sin (2 θ) + C

Solution steps

\int cos (2 θ) d θ

Apply u-substitution

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

= \int cos (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 cos (u) d u

Use the common integral:

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

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

Substitute back

u = 2 θ

= \frac{1}{2} sin (2 θ)

Add a constant to the solution

= \frac{1}{2} sin (2 θ) + C

f (x) = 3 x^{2} + 2 a x + b

y^{^{''}} - 2 y^{^{'}} + 5 y = 5 x + 3

x \to 3 lim (\frac{3 - x}{∣ x - 3 ∣})

\int (8 x + 1 - 9 e^{x}) d x

\frac{e ^{- s}}{s ^{2} + 3 s + 2}