Question

Solve, ∫cos(1/4 x) d x

Answer 1

The integral of cos(1/4 x) dx is solved using the integration rule for cosine, resulting in the solution 16sin((1/4)x) + C, where C is the constant of integration.

Step-by-step explanation:

To solve the integral ∫cos(⅔x) dx, we use the basic formula for integration of the cosine function. The integral of cos(ax) with respect to x is ⅔∫cos(ax) dx, which equals ⅔sin(ax)/a + C, where C is the constant of integration.

Applying this rule to our integral, we have:

1. Let a = 1/4. Then, our integral becomes ∫cos((1/4)x) dx.
2. According to the formula, the integral comes out to be (4sin((1/4)x))/(1/4) + C.
3. Simplifying, it becomes 16sin((1/4)x) + C.

Therefore, the solution to the integral of cos((1/4)x) with respect to x is 16sin((1/4)x) + C.