Question

What will be


\[\int\limits {(4x*y^2+6*y)/(-x^2y^2-2*x*y)} dx\]

Answer 1

is that y(x)? or is it independant as well?

Answer 2

4x+6
------- seems to be whats important if its a partial
-x^2-2x

Answer 3

i dont spose we can decomp that .....

Answer 4

I think you need to use partial fractions

Answer 5

In it both x and y are present

Answer 6

make variable change xy = z, and its easy

Answer 7

SAM how can we use partial fraction in it

Answer 8

xy =z, z' = y, 2zz' =2xy2

Answer 9

u get Ln(z2 +z)dz, and come back to xy

Answer 10

got it?

Answer 11

wait im tryin myko

Answer 12

kk

Answer 13

from,cancel common terms in the num and denom
\[\begin{array}{l} \text{ }\frac{4 x y^2+6 y}{-x^2 y^2-2 x y}\text{ } \\ \text{}

\int\limits -\frac{2 (2 x y+3)}{x (x y+2)} \, dx \\\end{array}\]
then use partial fractions:
you'll get
\[-2\int\limits \left(\frac{y}{2 (x y+2)}+\frac{3}{2 x}\right) \, dx\]
then integrate using u-sub

check if im wrong

Answer 14

\[\int\limits[2z+1/z ^{2}+z]dz = Ln (z ^{2}+z) + C\]

Answer 15

sry, forgot - sign

Answer 16

@Zarkon What's your opinion?

Answer 17

in front of integral

Answer 18

you are correct Sam

Answer 19

to complicated

Answer 20

\[Ans: -\ln (x y+2)-3 \ln (x)\]

Answer 21

\[\int\limits(2z+2/z ^{2}+2z)dz +\int\limits(4/z ^{2}+2z) dz = Ln (z ^{2}+2z)+ 4Ln(z+2)\]