Integrate x√(x^2)

To integrate x√(x^2), we can use the substitution method.

Let u = x^2
Then, du = 2x dx
Solving for dx, we get dx = du / (2x)

Now, we can rewrite the integral in terms of u:
∫x√(x^2) dx = ∫√u du / 2

Now, we can integrate √u with respect to u:
∫√u du / 2 = (1/2) * (2/3) * u^(3/2) + C
= (1/3)u^(3/2) + C
= (1/3)(x^2)^(3/2) + C
= (1/3)x^3 + C

Therefore, the integral of x√(x^2) is (1/3)x^3 + C, where C is the constant of integration.

∫x√(x^2) dx = ∫x^2 dx

= (x^3)/3 + C

where C is the constant of integration.