Question

Confusing problem need help ASAP

Answer 1

What is the problem?

Answer 2

\[\int\limits_{}^{}12(y ^{4}+4y ^{2}+1)^{2}(y ^{3} +2y)dy\]

Answer 3

@AravindG

Answer 4

@zepdrix

Answer 5

u=y^4+4y^2+1
du=4y^3+8y=4(y^3+2y)

Answer 6

yes

Answer 7

@eashy

Answer 8

integrate(12*u^2*du/4)
=integrate(3u^2 du)

Answer 9

Wait can we do step by step as i have just learnt this method

Answer 10

sure, first step is to find a good a u to pick
in this case, u=y^4+4y^2+1 works well (practice helps with this step)
next, find du in terms of dy. in this case, du=(4y^3+8y) dy
finally, replace all y's with u's and dx with du

Answer 11

I am getting just U^3 +C Is it correct

Answer 12

looks good.
remember to replace u's with y's at the end though
so u^3+c is really (y^4+4y^2+1)^3+C

Answer 13

yes thank you