Question

Anti derivative using u substitution for
\[\frac{6x}{(1+x^{2})^{2}\]

Answer 1

\[\frac{6x}{(1+x^{2})^{2}}\]

Answer 2

let u = 1+x^2

deriving both sides with respect to x gives

du/dx = 2x

du = 2x*dx

du/2 = x*dx

x*dx = du/2

6*x*dx = 6*du/2

6x*dx = 3du

so we go from

\[\int \frac{6x*dx}{(1+x^{2})^{2}}\]

to

\[\int \frac{3du}{u^{2}}\]

\[3\int \frac{1}{u^{2}}*du\]

Answer 3

do you see how to finish up?

Answer 4

umm give me a min.

Answer 5

ok

Answer 6

if you are stuck, then keep in mind that

\[\Large \frac{1}{u^{2}} = u^{-2}\]

Answer 7

so \[-\frac{3}{1+x^{2}}\]

Answer 8

don't forget the +C

Answer 9

oh I don't need the constant for the problem I'm working on but that you =)

Answer 10

*thank

Answer 11

otherwise,

\[\int \frac{6x*dx}{(1+x^{2})^{2}} = -\frac{3}{1+x^2}+C\]

is correct. Nice work

Answer 12

oh you're doing a definite integral (area under the curve), I see

Answer 13

yupp

Answer 14

you're welcome