# How do you evaluate the integral of #int (1 + cos 4x)^(3/2) dx#?

After a very long expansion, we get it into the following form

By signing up, you agree to our Terms of Service and Privacy Policy

To evaluate the integral (\int (1 + \cos(4x))^{3/2} , dx), you can use the trigonometric identity (\cos^2(x) = \frac{1 + \cos(2x)}{2}) to simplify the integral. Let (u = 1 + \cos(4x)), then (du = -4\sin(4x) , dx). Using the identity, you can rewrite (\cos(4x)) as (1 - 2\sin^2(2x)). Substituting (u) and (du) into the integral and simplifying will yield a form suitable for integration. You'll then integrate with respect to (u) and back-substitute to find the final answer.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the integral of #int (dx/sqrt(t^2-1))# from negative infinity to -2?
- How do you evaluate the integral #int xe^(-x^2)#?
- How do you find the definite integral of #t^3(1 + t^4)^3 dt# from #[-1, 1]#?
- How do you evaluate this trig integral #int 340cos^4(20x) dx#?
- How do you evaluate the integral from 0 to #pi/4# of #(1 + cos^2 x) / (cos^2 x) dx#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7