Use integration by substitution to solve the integral below. Use the C for the constant integration.

Question

f(sqrt 3x^4-4x+3)(12x^3-4)dx

Please help. I can send a picture of the equation if it’s confusing.

Answer 1

Substitute u = 3x^4 - 4x + 3

du/dx = 12x^3 - 4

dx = du / (12x^3 - 4)

Integral transforms to sqrt (u) (12x^3 - 4) dx = sqrt (u) (12x^3 -4) du / (12x^3 -4)

= sqrt (u) du

= u^1/2 du = 2/3 u ^3/2 + C

= 2/3 (3x^4 - 4x + 3 )^3/2 + C

Answer 2

Let u = 3x⁴ - 4x + 3

Differentiate both sides to get du = (12x³ - 4) dx

Next change all x's into u's by substituting, and take the integral with respect to u.

Substitute back into x.