What's the integral of x^7?

The integral of x^7 is (1/8)x^8 + C, where C is the constant of integration.

To find the integral of x^7, we 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. Applying this rule to x^7, we get:

∫x^7 dx = (1/8)x^8 + C

To check our answer, we can differentiate (1/8)x^8 + C with respect to x and see if we get x^7 as the result:

d/dx [(1/8)x^8 + C] = (1/8) * 8x^7 = x^7

Therefore, our answer is correct.

It's worth noting that the constant of integration, C, can take any value, since differentiating a constant always gives zero. This means that there are infinitely many antiderivatives of x^7, all of which differ by a constant.