What is the integral of (cos(x))^2-(sin(x))^2 ?

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

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integral of (cos(x))^2-(sin(x))^2

\int (cos (x))^{2} - (sin (x))^{2} d x

\frac{1}{2} sin (2 x) + C

Solution steps

\int (cos (x))^{2} - (sin (x))^{2} d x

Rewrite using trig identities

= \int cos (2 x) d x

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 x

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

Add a constant to the solution

= \frac{1}{2} sin (2 x) + C

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

\int 8 x + 9 d x

\int e^{θ} cos (2 θ) d θ

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

f (x) = x^{2} + 2, (- 3, 11)

What is the integral of (cos(x))^2-(sin(x))^2 ?
The integral of (cos(x))^2-(sin(x))^2 is 1/2 sin(2x)+C