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

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

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integral of-sin(x)cos(x)

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int u d u

= - \int u d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

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

Add a constant to the solution

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

\int \frac{e ^{3}}{x} d x

x \to 0 lim (\frac{∣ x ∣}{4 x})

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 36 y = 0

\int_{0}^{42} 2 - x^{\frac{2}{5}} d x

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