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

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

Popular >

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

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

- sin^{2} (x) + C

Solution steps

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

Apply u-substitution

: \int u d u

= - 2 \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

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

Simplify

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

= - sin^{2} (x)

Add a constant to the solution

= - sin^{2} (x) + C

\frac{\partial}{\partial x} (5 x^{2} y + 2 x y^{3} + 3 y^{2})

x^{^{''}} + x = 0, x (0) = 0, x^{^{'}} (0) = 0

\int_{- 4}^{4} (16 - x^{2}) d x

f (x) = x^{- 2}

\frac{d}{d x} (lo g_{10} (e^{x}))

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