What is the integral of sqrt(1-cos(2x)) ?

The integral of sqrt(1-cos(2x)) is -sqrt(2)cos(x)+C

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integral of sqrt(1-cos(2x))

\int 1 - cos (2 x) d x

- 2 cos (x) + C

Solution steps

\int 1 - cos (2 x) d x

Rewrite using trig identities

= \int 2 sin^{2} (x) d x

Take the constant out:

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

= 2 \cdot \int sin^{2} (x) d x

sin^{2} (x) = (sin (x)),

assuming

sin (x) \geq 0

= 2 \cdot \int sin (x) d x

Use the common integral:

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

= 2 (- cos (x))

Simplify

= - 2 cos (x)

Add a constant to the solution

= - 2 cos (x) + C

\int \frac{25 x ^{2} - 49}{x ^{3}} d x

\frac{d}{d x} (2 x - \frac{2}{x ^{3}})

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

\frac{e ^{x}}{2 x + 1}

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