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

x \to 0 lim (\frac{2 x}{∣ x ∣})

y^{^{''}} - 8 y^{^{'}} + 11 y = 0

\frac{d y}{d x} = (3 x y)

\int 4 x - x^{3} d x

i = 1 \sum \infty (\frac{1}{2})^{i - 1}

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