The integral ∫aa2+x2 dx is a standard form of integral that can be solved using a basic substitution method in calculus. Here are the steps to solve it:

Step 1: Let's substitute x = a*tan(θ). Then, dx = a*sec^2(θ) dθ.

Step 2: Substitute these values into the integral. We get ∫dθ = θ.

Step 3: Substitute θ back in terms of x. We know that tan(θ) = x/a, so θ = arctan(x/a).

So, the integral ∫aa2+x2 dx = arctan(x/a) + C, where C is the constant of integration.

Therefore, the correct answer is a. arctan(x/a). The other options b, c, d, and e are not correct.

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The integral ∫aa2+x2 dx is a standard form of integral that can be solved using a basic substitution method in calculus. Here are the steps to solve it:

Step 1: Let's substitute x = a*tan(θ). Then, dx = a*sec^2(θ) dθ.

Step 2: Substitute these values into the integral. We get ∫dθ = θ.

Step 3: Substitute θ back in terms of x. We know that tan(θ) = x/a, so θ = arctan(x/a).

So, the integral ∫aa2+x2 dx = arctan(x/a) + C, where C is the constant of integration.

Therefore, the correct answer is a. arctan(x/a). The other options b, c, d, and e are not correct.

Knowee AI · Accepted Answer

The integral ∫aa2+x2 dx is a standard form of integral that can be solved using a basic substitution method in calculus. Here are the steps to solve it:

Step 1: Let's substitute x = a*tan(θ). Then, dx = a*sec^2(θ) dθ.

Step 2: Substitute these values into the integral. We get ∫dθ = θ.

Step 3: Substitute θ back in terms of x. We know that tan(θ) = x/a, so θ = arctan(x/a).

So, the integral ∫aa2+x2 dx = arctan(x/a) + C, where C is the constant of integration.

Therefore, the correct answer is a. arctan(x/a). The other options b, c, d, and e are not correct.

Let a𝑎 be a positive real number. Then ∫aa2+x2 dx=∫𝑎𝑎2+𝑥2 𝑑𝑥=(select all that apply)Question 3Answera. arctan(xa)arctan(𝑥𝑎)b.aln(a2+x2)+c𝑎ln⁡(𝑎2+𝑥2)+𝑐c. 1aarccos(ax)1𝑎arccos(𝑎𝑥)d.1a2+x21𝑎2+𝑥2e. a2arcsin(xa)

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