What is the integral of cos(t)sin(t) ?

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

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integral of cos(t)sin(t)

\int cos (t) sin (t) d t

\frac{sin ^{2} ( t )}{2} + C

Solution steps

\int cos (t) sin (t) d t

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 (t)

= \frac{sin ^{2} ( t )}{2}

Add a constant to the solution

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

\frac{2 x ^{2} - 5 x + 5}{x - 2}

\frac{d}{d x} (f (x) sin (x))

x \to 0 lim (\frac{x}{8 x ^{2} - x})

\frac{d}{d x} (\frac{x - a}{1 + x})

f (x) = 2 (x)^{4}

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