What's the integral of x^5/2?

The integral of x^5/2 is (2/7)x^7/2 + C, where C is the constant of integration.

To find the integral of x^5/2, we can use the power rule of integration, which states that the integral of x^n is (1/(n+1))x^(n+1) + C, where C is the constant of integration. Using this rule, we can rewrite x^5/2 as x^(5/2) and apply the power rule to get:

∫ x^5/2 dx = (2/7) x^(7/2) + C

To check our answer, we can differentiate (2/7) x^(7/2) + C with respect to x using the power rule of differentiation, which states that the derivative of x^n is nx^(n-1). Differentiating (2/7) x^(7/2) + C gives:

d/dx [(2/7) x^(7/2) + C] = (2/7) * (7/2) * x^(5/2) + 0 = x^(5/2)

This confirms that our answer is correct.