Question

how to solve this integral ? (given below)

Answer 1

which integral?

Answer 2

\[\int ln(x^2)dx\]

Answer 3

Where did that come from lol.

Answer 4

from meh. solve it bb ;)

Answer 5

u sub :)

Answer 6

\[\int\limits \frac {v+v^2}{1-v^3} dv\]

Answer 7

power series.

Answer 8

break the integral up

Answer 9

\[\int \frac{v}{1-v^2} + \frac{v^2}{1-v^3}\]

Answer 10

typo...first integral is 1 - v^3

Answer 11

u sub won't work for first integral

Answer 12

u = 1 - v^3 => du / dv = -3v^2
while the the top is v, so it doesnt cancel out

Answer 13

for the first integral^

Answer 14

then what???

Answer 15

ok the first approach is to break it up then partial fractions on the first integrand, then u -sub for the other integral

second approach is to use partial fractions on the initial integral

Answer 16

so which approach u want to choose

Answer 17

1st one

Answer 18

ok it's gonna be long

partial fractions

- ((1-v)/3(v^2+v+1) + 1/3(v-1))

complete the square , then u-sub on the next integrand

Answer 19

the actual question was a differential eq: dy/dx = (x^2 + y^2 ) / (xy+ y^2)
i used y = vx and came to the integral which i posted here ... was i correct ?

Answer 20

@Mimi_x3

Answer 21

@digitalmonk I checked and got the exact same integral as you. Follow @Mimi_x3 's awesome advice and do it!

Answer 22

so this question is a step in a bigger question

Answer 23

ln (x^2) is 2 ln x
right ?

integral of ln x is pretty standard...or if needed to derive, use integration by parts :)

Answer 24

\[I=\int\limits \left( \ln x^2 \right)*1 ~dx\]
\[= \int\limits \left( 2 \ln x \right)*1 dx=2 \ln x *x- \int\limits \frac{ 2 }{ x }*x dx+c\]
i think now you can complete.

Answer 25

@eliassaab Did you even read the damn question?

Answer 26

@eliassaab Don't make yourself look like more of a fool than you already are. ;P