Evaluate the integral

Question

Evaluate the integral ∫x^6(x^7−8)^15 dx,

by making the appropriate substitution: u =  .

 

∫x^6(x^7−8)^15 dx  = 

 

NOTE: Your answer should be in terms of x and not u.

Answer 1

∫x^6(x^7−8)^15 dx = ∫(x⁷ - 8)¹⁵d(x⁷ - 8)/7 = 1/7(x⁷ - 8)¹⁶/16 + C = 1/112)x⁷ - 8)^{16 + C}