(x^3(x^2-1)^7)dx£?

Answer 1

Integration of [ x^3 (x^2 -1 )^7] , dx
Frst way U can expand using the bionomial theorm, then integrate
Or use the subistitution : x^2 -1 = y
then 2x dx = dy, x^2 = y +1
Then the integration will be :
Integ 1/2[ y^7 (y +1) dy]
= 1/2 integ. [ y^8 + y^7] dy
= 1/2 [ 1/9 y^9 + 1/8 y^8 ] + c
= 1/18 y^9 + 1/16 y^8 + c
= 1/18 (x^2 -1 )^9 + 1/16 (x^2 -1 )^8 + c

Answer 2

I assume that you are trying to integrate this and that the £ sign is a typing slip.
This is an example of integration by parts using the formula
int(u*dv/dx) = uv - int(v*du/dx) where u, v are each functions of x.
You have to choose which part of your original will be the u and which the dv. You make the u something that will get simpler when you differentiate it but the v gets no harder. Note that you will need to use integration by parts twice in this particular case.
That should be enough to get you started. Try to do it yourself before looking at anyone's detailed answer that they leave here.

Follow up having seen the next two answers. Yes, I did rather jump in without looking for an easier way to do it, so sorry. However, I still think that it is better to give people help with how to answer a question themselves rather than give every line of the working to the answer.

Answer 3

=3x^2(x^2-1)^7+x^3(7(x^2-1)^6(2x))