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

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

\frac{d}{d x} (\frac{4 x ^{2} + 8 x + 2}{x})

x^{2} \frac{d y}{d x} + sin (x) - y = 0

x \to + 0 lim (3 x^{2})

\frac{d y}{d x} = y sin (2 x)

\int \frac{3 a x}{b ^{2} + c ^{2} x ^{2}} d x

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