The discussion revolves around the integration of the expression ∫(3x^2+x)(2x^3+x^2)^2 dx, focusing on the use of substitution methods in calculus.
Some participants have provided guidance on the substitution process and clarified the relationship between the differentials. There appears to be a growing understanding among participants, although not all aspects have been fully resolved.
Participants express confusion regarding the transition from the substitution to the integral form, particularly in understanding the factor of 1/2 in the integral expression.
Nanu Nana said:Homework Statement
dz/dx=(3x2+x)(2x^3+x^2)^2[/B]Homework Equations
∫(3x^2+x)(2x^3+x^2)^2 dx
The Attempt at a Solution
I tried substituting (2x^3+x^2)
Let t= 2x^3 + x^2
dt=6x^2+2x dx
dt/dx= 6x^2+2x
I can only solve till this point . I don't have any clue how to solve it further
But how do we get 1/2 ∫u^2 du ?? I don't understand it at all
Well, you used t as a variable rather than u, but that's unimportant.Nanu Nana said:Homework Statement
dz/dx=(3x2+x)(2x^3+x^2)^2[/B]
Homework Equations
∫(3x^2+x)(2x^3+x^2)^2 dx
The Attempt at a Solution
I tried substituting (2x^3+x^2)
Let t= 2x^3 + x^2
dt=6x^2+2x dx
dt/dx= 6x^2+2x
I can only solve till this point . I don't have any clue how to solve it further
But how do we get 1/2 ∫u^2 du ?? I don't understand it at all