# How do you find the Integral of #sqrt(x^2 - 16)/ x dx#?

Using the trigonometric substitution technique of integration we eventually get

I will use the trigonometric substitution technique of integration to solve this integral.

Therefore the original integral becomes :

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

To find the integral of √(x^2 - 16)/x dx, you can use trigonometric substitution. Let x = 4sec(θ). Then dx = 4sec(θ)tan(θ) dθ. Substituting these into the integral yields: ∫(4sec(θ))^2/(4sec(θ))tan(θ) dθ = ∫4sec^2(θ)/4tan(θ)sec(θ) dθ = ∫sec^2(θ)/tan(θ) dθ. Since sec^2(θ)/tan(θ) = sec(θ)sin(θ), the integral becomes ∫sec(θ)sin(θ) dθ. Using the identity sec(θ) = 1/cos(θ), this becomes ∫(1/cos(θ))(sin(θ)) dθ. Integrating this expression yields the final result: ln|sec(θ) + tan(θ)| + C, where C is the constant of integration. Finally, substitute back x = 4sec(θ) to obtain the integral in terms of x.

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

- How do you integrate #int x/sqrt(3x^2-6x+10) dx# using trigonometric substitution?
- How do you integrate #int x^2lnx# by integration by parts method?
- How do you integrate #f(x)=(x^2-2)/((x+4)(x-2)(x-2))# using partial fractions?
- How do you integrate #sec(x)/(4-3tan(x)) dx#?
- How do I find the antiderivative of #f(x)=secxtanx(1+secx)#?

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