please help me with this using POLYNOMIAL FUNCTIONS USING SUBSTITUTION RULE (with solution pleaseee)

Question

1. ∫ x √2x²-9 dx
2. ∫ x³ (1+3x⁴)⁵dx

Answer 1

1. Let u = 2x²-9 Then du = 4xdx. So, xdx = (1/4)du

So, ∫x√(2x²-9)dx = (1/4)∫u^1/2du = (1/6)u^3/2 + C = (1/6)(2x²-9)^3/2 + C

For the second problem, Let u = 1 + 3x⁴ Then du = 12x³dx. So, x³dx = (1/12)du

So, ∫x³(1+3x⁴)⁵dx = (1/12)∫u⁵du = (1/72)u⁶ + C = (1/72)(1+3x⁴)⁶ + C