Find the Antiderivative h(t)=6cos(t)

$h (t) = 6 \cos (t)$

The function $H (t)$ can be found by finding the indefinite integral of the derivative $h (t)$ .

$H (t) = \int h (t) d t$

Set up the integral to solve.

$H (t) = \int 6 \cos (t) d t$

Since $6$ is constant with respect to $t$ , move $6$ out of the integral.

$6 \int \cos (t) d t$

The integral of $\cos (t)$ with respect to $t$ is $\sin (t)$ .

$6 (\sin (t) + C)$

Simplify.

$6 \sin (t) + C$

The answer is the antiderivative of the function $h (t) = 6 \cos (t)$ .

$H (t) =$ $6 \sin (t) + C$