## swin2013 2 years ago Integral with U sub!

1. swin2013

integral y^2 (1+y)^2 dy

2. swin2013

My work: u = 1+y du/dy = 1 du=dy?

3. swin2013

then integral (1+y)^2 dy integral u^2 du

4. swin2013

(1_y)^3/3 +c

5. swin2013

*(1+y)^3

6. swin2013

do i keep the y^2?

7. swin2013

ohh ok.. but what about u sub?

8. swin2013

will u now be y^2+y^4?

9. swin2013

well my teacher made this worksheet specifically for u sub :(

10. swin2013

but i got 1 for u sub anyways. so i just keep y^2 ?

11. swin2013

no

12. swin2013

it's y^2 (1+y)^2

13. swin2013

the square is outside the parenthesis

14. stamp

I see my mistake. Let me reevaluate the problem and I will come at you with a response.

15. zepdrix

Yah you wouldn't use a `U sub` for this one I'm afraid swin. You would just expand out the brackets and integrate each term individually.

16. stamp

\[y^2(1+y)^2dy=y^2(y^2+2y+1)dy=(y^4+2y^3+y^2)dy\]

17. swin2013

i didn;t know i had to lol oops

18. swin2013

is there an indication to do so?

19. stamp

No, you are simplifying your y terms and happen to end up with \[ (y^4+2y^3+y^2)dy \]Integrate each term dy

20. swin2013

oh ok. that makes sense. usually i don't have to expand a problem or distribute so i didn't know if using u sub for 1+y is correct

21. stamp

Had you done some usub, you would had \[(y^2u)du\] and would not really have gotten anywhere as far as the integral goes. Be sure to have + C to your integral term since the integral is undefined.

22. zepdrix

To apply a `u sub`, you want to look for a suitable `u` and `u'` somewhere in your problem. \(2y(1+y^2)\) See how if \(u=1+y^2\) then \(u'=2y\) ? In the problem you were given, letting your inner function be `u` did NOT result in the outer function being u'. So that is usually your indicator.

23. swin2013

OHH ok! I'll make sure to tell my teacher to clarify this to the class. I did not know that! hahaha

24. swin2013

oh but in the case you're presenting it's (1+y^2) not (1+y)^2

25. swin2013

u sub can be used when the exponent is outside right?