What is the integral of-4sin(x)cos(x) ?

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

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integral of-4sin(x)cos(x)

\int - 4 sin (x) cos (x) d x

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

Solution steps

\int - 4 sin (x) cos (x) d x

Take the constant out:

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

= - 4 \cdot \int sin (x) cos (x) d x

Apply u-substitution

= - 4 \cdot \int u d u

Apply the Power Rule

= - 4 \cdot \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= - 4 \cdot \frac{sin ^{2} ( x )}{2}

Simplify

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

= - 2 sin^{2} (x)

Add a constant to the solution

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

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