Question

Find Integral of (1/((a²)+(u²))).

Answer 1

The integral of (1/((a²)+(u²))) can be found using trigonometric substitution. The result is (1 / a²) θ + C.

Step-by-step explanation:

To find the integral of (1/((a²)+(u²))), we can use the trigonometric substitution method. Let's substitute u = tan(θ). Then, du = sec²(θ) dθ. Next, replace (a²) + (u²) with a²sec²(θ). The integral becomes:

∫ (1 / (a²sec²(θ))) * sec²(θ) dθ

Simplifying further, we get:

∫ (1 / a²) dθ

Finally, integrating with respect to θ, we get:

(1 / a²) θ + C

where C is the constant of integration.