Question

Using The Method Of Substitution, I=∫X2(1+2x3)2dx=∫F(U)Du Where

U=____ Du=_______F(U)=_________

Answer 1

The method of substitution for the integral of x^2(1 + 2x^3)^2 dx involves setting u = 1 + 2x^3, finding du = 6x^2 dx, and substituting in to get the integral as a function of u.

Step-by-step explanation:

The student is asking how to perform integration by substitution for the integral I = ∫ x^2(1 + 2x^3)^2 dx. For substitution, we let u = 1 + 2x^3, thus du = 6x^2 dx.

Dividing both sides of the equation for 'du' by 6, we get du/6 = x^2 dx, which can be used to replace x^2 dx in the original integral. Thus, the integral becomes I = ∫ (u-1)^2/3 * (du/6), with F(u) = (u-1)^2/3.