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

The integral of (1-cos(2x))sin(2x) is sin^4(x)+C

Popular >

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

\int (1 - cos (2 x)) sin (2 x) d x

sin^{4} (x) + C

Solution steps

\int (1 - cos (2 x)) sin (2 x) d x

Apply u-substitution

: \int \frac{u}{2} d u

= \int \frac{u}{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 u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{1}{2} \cdot \frac{u ^{2}}{2}

Substitute back

u = 1 - cos (2 x)

= \frac{1}{2} \cdot \frac{( 1 - cos ( 2 x ) ) ^{2}}{2}

Simplify

\frac{1}{2} \cdot \frac{( 1 - cos ( 2 x ) ) ^{2}}{2} : sin^{4} (x)

= sin^{4} (x)

Add a constant to the solution

= sin^{4} (x) + C

\int \frac{x y}{1 + x ^{4}} d y

\int x x^{2} + 6 x + 9 d x

\int \frac{4 cosh ( x )}{x} d x

\int \frac{21 x - 12}{x} d x

\int \frac{3}{x + 2} d x

What is the integral of (1-cos(2x))sin(2x) ?
The integral of (1-cos(2x))sin(2x) is sin^4(x)+C