Question

Find the integral of 1/ √x²+ a² with respect to x

Answer 1

To find the integral of 1/√x² + a² with respect to x, you can use a trigonometric substitution. Let's substitute x = a tan θ. Then, dx = a sec² θ dθ. Plugging these substitutions into the integral, we get: ∫ 1/√(a² tan² θ + a²) * a sec² θ dθ. Next, simplify the integral using trigonometric identities. The integral becomes: ∫ cos θ dθ = sin θ + C, where C is the constant of integration. Now, substitute x back in for θ to get the final answer: sin(a tan⁡⁡⁡⁡ θ) + C.

Step-by-step explanation:

To find the integral of 1/√x² + a² with respect to x, you can use a trigonometric substitution. Let's substitute x = a tan θ. Then, dx = a sec² θ dθ. Plugging these substitutions into the integral, we get:

∫ 1/√(a² tan² θ + a²) * a sec² θ dθ.

Next, simplify the integral using trigonometric identities. The integral becomes:

∫ cos θ dθ = sin θ + C,

where C is the constant of integration. Now, substitute x back in for θ to get the final answer: sin(a tan⁡⁡⁡⁡ θ) + C.