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

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

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

integral

cos^{2} (x) - sin^{2} (x)

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

Solution steps

\int cos^{2} (x) - sin^{2} (x) 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{( 1 - x )}{( x + 2 )}

5 + 2 x

\frac{( 1 + sin ( x ) )}{cos ( x )}

\frac{( x - 1 )}{( x + 1 )}

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

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