Question

\[\int {3 \over 5y + 4}dy\]

Answer 1

I'd first take \(u = 5y + 4\), then \(du = 5dy\)?

Answer 2

yup

Answer 3

So,\[dy = {1 \over 5}du\]

Answer 4

yeah, then you are almost done!

Answer 5

OK, let's make the substitutions.\[{1 \over 5}\int{3 \over u}du \]

Answer 6

you can also take the 3 out of the integral

Answer 7

Yes, doing that.\[{3 \over 5}\int{1 \over u} du \]

Answer 8

So ln(u) inside?

Answer 9

\[{3 \over 5} \ln(u) + c \]Is that correct?

Answer 10

now sub back in for u

Answer 11

And then substituting back,\[ {3 \over 5}\ln(5y +4) + c\]

Answer 12

Right?

Answer 13

yessir :)

Answer 14

Thank you :)

Answer 15

more accurately its 3/5 ln |5y+4| + c

Answer 16

Oh... I forgot the |...| brackets.

Answer 17

those brackets should be there with ln everytime.