# How do you integrate #sqrt(1+(4cos^2))dx#?

If you are not in a very advanced Calculus course, where you might work with elliptic integrals, you don't have to know how to do this analytically. At best you can do a numeric integral.

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

To integrate √(1 + 4cos^2(x)) dx, you can use the trigonometric identity cos^2(x) = (1 + cos(2x))/2:

√(1 + 4cos^2(x)) dx = √(1 + 4(1 + cos(2x))/2) dx = √(1 + 2 + 2cos(2x)) dx = √(3 + 2cos(2x)) dx

Now, let u = 2x, then du = 2dx:

= (1/2)√(3 + cos(u)) du

Now, integrate (1/2)√(3 + cos(u)) du with respect to u, then substitute back u = 2x to obtain the final result.

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 use integration by parts to establish the reduction formula #intsin^n(x) dx = -(1/n)sin^(n-1)(x)cos(x)+(n-1)/nintsin^(n-2)(x)dx# ?
- How do you integrate #(1x^(2)+4x+12)/((x+2)(x^(2)+4)) # using partial fractions?
- What is #f(x) = int sec^2x- cosx dx# if #f((5pi)/4) = 0 #?
- How do you find the integral #ln(x) x^(3/2) dx#?
- How do you integrate #int (x+1)/[(x^2+1)^2(x^2)]# using partial fractions?

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