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))

\int (cos^{2} (x) - sin^{2} (x)) d 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{\partial}{\partial x} (\frac{9 x}{x ^{2} + 5 y})

2 x - \frac{1}{2 x}

\int_{0}^{1} 9 x^{2} + 1 d x

\int sec (\frac{2 x}{5}) tan (\frac{2 x}{5}) d x

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