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

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

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integral of-cos(x)sin(x)

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

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

Solution steps

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

Take the constant out:

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

= - \int cos (x) sin (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

f (x) = 5 x + 1

\int_{\frac{1}{7}}^{5} 4 x ln (7 x) d x

f (x) = \frac{9}{x ^{2} + 5}

f (x) = \frac{( tan ( x ) - 1 )}{sec ( x )}

\int_{0}^{3} \frac{1}{2 x + 3} d x

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