# Find the Antiderivative cos(1/2x)

Write the polynomial as a function of .
The function can be found by finding the indefinite integral of the derivative .
Set up the integral to solve.
Let . Then , so . Rewrite using and .
Let . Find .
Differentiate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Rewrite the problem using and .
Simplify.
Multiply by the reciprocal of the fraction to divide by .
Multiply by .
Move to the left of .
Since is constant with respect to , move out of the integral.
The integral of with respect to is .
Simplify.
Replace all occurrences of with .
The answer is the antiderivative of the function .
Find the Antiderivative cos(1/2x)