integral problem?

Question

integrate

x / (x+2)

Answer 1

Integral [(x / (x + 2)) dx]

One way you can solve it (I can immediately think of at least two) is to use substitution.

Let u = x + 2. Then
u - 2 = x, so
du = dx.

Making the appropriate substitution, we get

Integral [(u - 2) / u ] du

Which we can separate into two fractions.

Integral [u/u - 2/u] du

Integral [1 - 2/u] du

Integral [1 - 2(1/u)] du

Which we can now integrate directly, as

u - 2ln|u| + C

Substituting u = x + 2 back, we have

x + 2 - 2 ln |x + 2| + C

Answer 2

x/(x+2)

by adding 0 to the numerator (2-2) you can rewrite it as

S(x+2-2)/(x+2) dx

then you can break it into two separate integrals

S(x+2)/(x+2) dx - S2/(x+2) dx
S1 dx - 2 S 1/(x+2) dx
x - 2 ln |x+2| +C

Answer 3

wang?
Flatulence is not detrimental the society's needs.
For the release of monumental evacuations of flatulence can protect us from the upcoming ice age.
The ozone layer only wants to be our friend, so I say let him have his day in the sun (comparatively to us humanoids on planet Earth).

Answer 4

primitive(x / (x+2))= primitive((x+2)/(x+2)-2/(x+2))=x-2* primitive(1/(x+2))+C=x-2*ln(x+2)+C