Question

integrate loge y

Answer 1

what?

Answer 2

huh?

Answer 3

is it impossible to do?

Answer 4

i just dont kno what u have written.
is it log(e*y) or log(e)*y?

Answer 5

log(e)*y

Answer 6

yes

Answer 7

you mean
\[\int \ln(y)dy\]?

Answer 8

yes@satellite73

Answer 9

if so answer is
\[y\ln(y)-y\]

Answer 10

integration by parts, but this is such a common integral that it is best just to remember it

Answer 11

@ satellite can you please show me your steps
thx

Answer 12

ok do you know how to integrate by parts?

Answer 13

no sorry

Answer 14

usually written as
\[\int udv=uv-\int vdu\]

Answer 15

basically it is the reverse of the product rule. so in this case it is kind of a trick. you put
\[u=ln(x)\]
\[du=\frac{1}{x}dx\]
\[dv=1\]
\[v=x\] and use the formula to get
\[\int ln(x)dx = x\ln(x)-\int x\times \frac{1}{x}dx\]

Answer 16

i.e.
\[\int \ln(x)dx = xln(x)-\int 1dx = x\ln(x)-x\]

Answer 17

the checks is taking the derivative of
\[x\ln(x) -x\] using the product rule and see that you get
\[ln(x)\] back. this check also helps explain why integration by parts works

Answer 18

oh i see thanks