Evaluate the indefinite integral. (Use C for the constant of integration.)

Question

x⁷/1+x¹⁶ dx

Answer 1

∫[x⁷ / (1 + x¹⁶)]dx = ∫[x⁷ / (1 + (x⁸)²]dx

Let u = x⁸. Then, du = 8x⁷dx. So, x⁷dx = (1/8)du.

Thus, we have (1/8)∫[du / (1 + u²)] = (1/8)Tan^-1u + C = (1/8)Tan^-1(x⁸) + C