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{4 x}{( x ^{2} + 1 )}

\int_{1}^{8} x^{\frac{- 2}{3}} d x

e^{- x} sin (x)

f (x) = \frac{e ^{x}}{5 - 2 x}

\frac{d}{d x} (e^{x s i n (2 x)})

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